Driveability-wise, 2WD is more difficult to floor it but has less rotating parts and doesn't build up speed quite as easily, so is maintenance friendly; 4WD is easier to drive, but invites to go too far and too fast. It may also require more maintenance.
For 2WD, I would say you can't beat the Associated RC10B5 (the rear-motor one)... It's a very good quality car from both performance and durability perspective. The trend for racing has gone towards mid-motor cars... It seems Associated anticipated for better rear-motor sales when they put the RC10B5 on the market, so these are up for grabs at very good prices - I was lucky to get one for 100GBP new in box, but with 120GBP you should be on target for one
For 4WD, I would go shaft-drive for bashing purposes (it's more durable and usually the transmission is closed). If you're willing to go second hand, the Team Durango DEX410 may be a car to consider: It's a bit tight for space, but it's a durable car, they're cheap and plentiful second-hand. Spare parts are expensive from Durango, but again the second-hand market is quite good here... A new 4WD at 120GBP might be a bit tough if you'd like something that will stay in one piece.