The 998cc engine is a very robust and tunable unit. It is also the most common engine found in standard Minis.

See bottom for useful part numbers

Terminology:
MSC/MM - Mini Spares Centre/Mini Mania
ID            - Inside Diameter
OD          - Outside Diameter
BBU         - Big Bore Unit (refers to all 1275cc-based units) 
SBU         - Small Bore Unit (refers to all sub-1275cc units, here the 998)
BHP         - Brake Horse Power
LCB         - Long Centre Branch

Despite the lure of the much-advertised 1380cc alternatives, many simply want to get a little more from what they have at reasonable outlay.
The single biggest restriction on any standard Mini is the 'breathing apparatus' - anything that is connected to the induction and exhaust systems. The standard exhaust being the biggest culprit - it is desperately restrictive in the name of noise suppression and cheapness of manufacture. Oddly enough it also increases fuel consumption when tested over a better designed, free-flowing unit, so this is the place to start - NOT I stress the intake which is where many start in the belief that's the way to go. It is not. It is definitely the EASIEST place to start, and possible the cheapest - but will
net less gain for your money. Your best budget-verses-gain improvements should therefore be done in 'reverse' order - starting at the end of the exhaust then working your way back to the air filter.

Exhaust System.
The key here is not to use something that is too big, as this will actually loose power. Unfortunately it is a pitfall far too many fall into in the belief that 'biggest is best', and the recent crop of dirt-cheap, 2.0" systems. They are made 2.0" for two reasons - Mini owners seem to be impressed by the '2.0" exhaust' term, and the manufacturers believe they are making a more efficient system as it slides over the tail-end of most commonly used LCBs. For further reasons 'why', see 'Exhausts - sizing and styles'.

It is entirely possible to fit an efficient system on it's own to the standard manifold as Mini Spares/Mania can supply an adaptor for just such an application. This replaces the flared front down-pipe section from the cast iron manifold down to under the car to mate up with the RC40. They used to do just a short adaptor sleeve to fit the standard down-pipe but almost all folk found the flared end of their standard one had broken off once they'd got around to doing the job - so the adaptor was dropped as a pointless exercise. 

1.625" internal bore is as big as you need to go on an SBU to get the very last drop of power out - even on a full-race engine. My recommendation here is the twin box RC40 - simply because in all the years it has been around - nobody has managed to better it's performance. And I've tried just about every last one that's come on the market. The only one that gets very close is the latest Millennium system from MSC/MM. The benefit of the Millennium exhausts for those who are aesthetically selective is the choice of 'exit' pipes and styles. The RC40 is available in single box form for those wanting a 'sportier' exhaust note, but is slightly less efficient than the full twin box - loosing a couple of BHP and shortens/lowers the torque curve.

Exhaust Manifold.
Progressing back along our route to power, the exhaust manifold is next. The standard iron one isn't too bad for an entirely standard engine, but is less efficient than the standard iron inlet manifold. The fact they are cast as one causes power losses on it's own by creating a severe, power robbing 'hot spot' in the inlet tract. Since separating them is only possible by destroying one or the other, loose the exhaust manifold.

Generally I use and highly recommend the Maniflow 'Cooper Freeflow ' exhaust manifold on SBUs. Originally developed by Maniflow owner Dave Dorrington when he was at Downton Engineering for the 970 S, it definitely has sufficient flow to cope with just about anything a 998 will could throw at it, and is easier to fit/seal than an LCB. Its design also suits the SBUs torque/power curve better than the commonly used LCB. And that's another common pitfall - fitting an LCB to the SBU. Some vendors sell what has become commonly termed the 'standard bore' LCB to fit everything - for exactly the same reasons they sell the 2.0" exhaust systems - it's what the misinformed Mini owners ask for, and there is a very cheaply made 'budget' example available that costs less than a Cooper Freeflow. This 'standard bore' LCB is in fact a 'medium bore' LCB developed for the BBU so is simply too big for the road-going SBU. In back to back tests I've done with this budget LCB and the Cooper Freeflow, I've always found the Freeflow gives better results. Not to mention the fact they last a hell of a lot longer through quality manufacture too!
I also use an LCB on SBU for the road, but this is the pukka small-bore LCB developed by Maniflow specifically for the SBU. The primary and secondary pipes are smaller, as is the tail-piece (fish-tail, 'Y'-piece). It does produce slightly better torque/power curves than the Freeflow but is marginally more expensive and less easy to seal off properly. 

Inlet Manifold.
Although the standard iron inlet manifold is reasonably good, a well-designed and proportioned one will better it. The iron one's main problem is it's internal sizing - it's too big for the SBU. The MSC/MM aluminum manifold out-performs the standard one by quite a margin in all areas, maximizing airflow and gas-speed within the very prohibitive space. The parameters for the manifold were to set to allow the use on the standard air filter case should this be required, and this has been met.
It also has the facility for water heating (not cooling as some folk believe). This is essentially to provide trouble-free running where cooler climates are to be experienced. Although having the intake temperature as low as is possible without actually freezing the fuel out of the air gives maximum torque/power, some manifold heating is required where climates are sufficiently cool enough to cause frost or heavy, cold misting. Cold wet air causing the biggest problems. Plumbing it into the system is a cinch - just take the hose off the heater tap and connect it to the left side of the manifold, than get a short piece of hose to re-connect the heater tap to the right side of the manifold (for further detailed information, see 'Inlet manifolds - single SU'').

Air Filters.
The standard air filter casing is surprisingly effective and efficient. Utilizing
this with a replacement K&N air filter will provide pretty much all the airflow the engine will need, even when fairly well tuned. All that is needed to
maximize the performance is to remove the hot-air 'snorkel', and drill a half-dozen three-quarter-inch diameter holes around the front underside of the casing. Ensuring these holes are OUTSIDE the cleaner element of course! The bonus of retaining the standard casing is the civilized noise level it provides in comparison to the cone/pancake type K&N…

It may look prettier - but that cone/pancake makes a mighty row. It's OK at idle, and tolerable when cruising at low speed, but any load or high- speed motoring creates an ear-bleeding din. Not only that, sorting the fuelling can be very arduous, AND recent testing has proven that this et-up actually LOOSES power over the aforementioned by around 5%! Now that's definitely not good.

The Holistic Answer.
The ingredients described above when added together comprise the 'stage one kit'. Although the above can be done one piece at a time if the budget is VERY tight, the complete stage one kit with all necessary gaskets and new carb needle required to provide correct fuelling only costs a comparatively small sum. The main benefit of doing it all in one go is actually reducing costs. Doing the job a piece at a time will involve re-tuning at each stage with the associated costs (carb needle, gaskets, etc.). Not to mention the aggravation of having to cut the manifolds apart - a very tiresome job! And you get the full power increase in one hit!

I developed the stage one kit for MSC many years ago to deal with just such tuning exercises. I used my every day 998 Mini. I took it to Peter Baldwin's rolling road, optimized the performance of the standard unit then took some power readings. Off the rollers and up in the air, the Mini had the aforementioned components fitted then went back on the rollers. Again performance was maximized, the new power readings recorded. The needle type was kept as a standard, available as stock replacement so it was repeatable indefinitely. Filing one was no good as it's impossible to file two the same, let alone multitudes! The new ignition setting was duly noted also. The kit was then tried on several other 998 Mini with different engine specs/ages, and all results recorded and compared. The stage one kit gave essentially identical improvements on each engine.

Power Gains.
Using figures when discussing power gains is pointless. The improvements entirely depend on each individual engine's output prior to tuning. These vary considerably because of various factors - such as engine mileage, how well it's been maintained, low or high compression, pre-A+ or A+, and so on. We therefore use percentages, as these are more realistic and comparable.

I haven't tried testing each item as a replacement and seeing what power increases each made - the exercise would simply be too expensive. In fact it would cost something like three times the cost of a stage one kit! And the claims made by certain component manufacturers are unfounded. For instance - K&N would have you believe fitting a cone/pancake filter would unleash 6bhp. That would represent a gain of 14% all on it's own! Considering the WHOLE stage one kit gives 20% extra, and the exhaust is the most restricting component in the whole induction/exhaust system - the claim is impossible. It's more likely that replacing the exhaust would
net a 12% gain, the rest down to the induction.

My recommendation then is to go for the stage one kit first hit. If the budget is tight, borrow the money or save up - it won't break the bank and you'll get the best improvement in one shot with a great deal less hassle. The MSC/MM stage one kit contains all the right ingredients - K&N replacement air filter, high-performance water-heated inlet manifold, Maniflow Cooper Freeflow exhaust manifold, RC40 twin-box exhaust system, complete exhaust hanger kit, replacement
carb needle, all gaskets and fitting instructions. It takes about 2.5 hours to fit taking things easy.

By way of a warning - some vendors advertise greater than 20% power gains. I'd like to see the proof of this as I've never seen more than 22% on one engine only where the exhaust was in particularly bad shape! I find it really hard to believe that a consistent 25% is possible. Only maybe on a one-off.

Useful part numbers:
C-STN17 Complete stage one kit
RC40          RC40 twin-box exhaust system
RC40-051    Stainless steel rear box
RC40-060    Stainless steel centre box and down-pipe for above
C-STR809    RC40 rear box only
AN180V       Exhaust pipe required when fitting single rear box
RC40FK       Complete RC40 fitting kit 
C-STR816    Cooper Freeflow exhaust manifold
C-STR817    Small-bore LCB exhaust manifold
LDP1          Front repair/conversion down-pipe for RC40 to standard  exhaust manifold 
C-AHT770 Aluminum inlet manifold, 1.5" single SU carb
E2601         K&N replacement air filter element
56-9320      K&N cone filter
AJM601      Exhaust manifold gasket
AEC2083 Carb to manifold and throttle abutment plate gasket (3 required)
CUD1018    AAU needle for stage one kit with replacement element air filter - non-modified casing
CUD1011    AAM needle for stage one kit with replacement element air  filter - modified casing (with holes drilled in)

For full Millennium range of exhaust options, see stock listing.