The 850 should be regarded as the true 'classic' Mini. It was the original and was what set the car out from the rest of the small cars of the early 1960's.
In fact, they are a joy to own and drive, giving the real 'retro-driving' experience from that time.
'In the day' a lot of 850's were improved and the above advice is good.
A nice specification would be:
A 295 head well gas-flowed & skimmed to give the best possible CR which is around 9.5:1. Better pistons if you can find a set, a Kent 256 cam, a 3-into-1 exhaust manifold with a 998 Cooper exhaust pipe, a pair of HS2 carbs, or a single HS4 on aflowed and matched inlet manifold, a slightly lightened flywheel.
Have it all balanced and keep the revs below about 6200 rpm to preserve the crankshaft.
With all that you should be getting somewhere near 50 bhp at around 5600 rpm and with that the old 850 will go very nicely.