Haven't bought one yet actually. Plan is to buy a shell and buy all the mechanical components. If I don't get a shell, I'll just buy a normal one and remove the parts. Idea so far:
-champ motor and gearbox
-change to rear wheel with prop and diff
-replace brakes with something easily available?
-suspension - No clue what to do yet
Basically I want to remove original mini mechanical parts and replace it with, reliable, easy to find parts...
Having owned a few Mini's in my day....
-champ motor and gearbox
I've seen a Champ motor in a Mini, but that was in a Oval track racer.
(It's worth noting that the Champ motor is basically an evolution of the A-Series motor found in the Mini anyway)
Gearbox - No, will never fit. (five speed boxes are available from the UK)
Champ Engine is mounted longitudinally, the Mini's is transversely mounted. Simply not enough space to mount an A-series Motor longitudinally.
-change to rear wheel with prop and diff
No no no! Mini has an independent rear suspension (which in part accounts for it's superb road holding). The body shell won't accommodate the drive shaft and once you get to the back, there is no axle to mount it onto.
-replace brakes with something easily available?
Change to discs if you can, but remember Mini wheels and arches are smaller than just about every other car out there. (pirate parts were readily available last I looked)
-suspension - No clue what to do yet
Do nothing. Replace shocks, and replace rubber blocks if required (There are no springs). Nothing you can do to a Mini suspension. will improve handling.
Like others I suggest you get a refurbished 1275 motor. In standard form it will get you to 140km very quickly (it's the lack of a 5th gear which stops you there, not power) and they are reliable. A bored out 1275 won't produce much less power than a Champ motor.
If you can source a 5 speed gear box then a better route to more power is a low boost Turbo or a supercharger. (seen both done reliably)
One thing you can do is improve engine cooling, especially if you're turbo charging, I once saw a neat installation of a Golf III radiator in the front grill of a Clubman body as an addition to the existing radiator.
The key thing to remember is that Mini's are fun to drive not because they go fast (they don't really), but because they are fast around corners. Tight corners curvy roads are a Mini's natural habitat and that is due to front wheel drive and independent suspension (no Axle).
Please don't hack a mini -shell to bits to defeat the whole purpose of the design (which was 30 years ahead of it's time)