[Si Coe]

You can use lipos with brushed esc's, and the performance difference over NiMH is incredible. However, lipos need very different care than NiMH's and chief amongst that is they should never be discharged. Virtually all brushless esc's and a few modern brushed ones have a low voltage cutoff that prevents this happening - without it you risk ruining your pack. This is not a major issue when racing as you'll never use a whole pack in a 5 min race, but can be a problem when you practice.
Apart from being a bit quicker, lipos are also cheaper overall. They last longer than NiMH's, and don't mind being used more than once a day. Most racers I know have only 1 or 2 packs tops and simply top them up between heats.

The gearing will depend on the motor and track. Therefore I'd need more information.

There is not much 'stock' racing goes on in buggys anymore. Brushless and Lipo has made full on modified no more expensive than stock. For very little money anyone can have a buggy as fast as they can control, so thats what we all do.