My daughter had a 1979 brown 850 when she was about 20. She named it 'Charlie Brown'. it was a great little car.
For 850 performance the drum brakes are adequate so long as the cylinders, linings, drums and adjusters are all in good condition.
It is always worthwhile replacing the suspension bushes on the front and making sure all the suspension settings are correct.
The cylinder head on the 850 will give a decent power increase if gas-flowed. The Cooper 12G295 head can be fitted, but it would be expensive and would need a lot skimming off it to get the CR to even a reasonable figure. Best to do some work on the original 850 head and skim it to get the CR to around 9.75:1.
A 3-into-1 exhaust manifold is a good idea, but don't heat-wrap it as that leads to all sots of problems with welds cracking. The original Cooper exhaust pipe is also good as it is not too big in diameter.
With a better head, an HS4 carb, suitably 'needled' improves things so long as a better inlet manifold is used.
The 850 is a lovely true classic car and is just fun to drive. Mini motoring as it was intended to be. With the 3.5" x 10" wheels the handling is about the best you can ever get from a Mini and much better than the later cars with huge wide wheels.
You will simply love driving it. Good luck.