I'm not really sure about battery choice, but perhaps a couple of sport stickpacks would be a decent enough starting point.
For the motor and speedo, I would definitely consider a brushless setup. Brushless doesn't necessarily mean fast.
Brushed is almost a thing of the past now (Might get slated for saying that!). Motor maintenance isn't fun, and the last thing you want to be doing is replacing brushless and skimming commutators after every 3-4 sets of cells through the motor.
If you'd prefer to buy new, LRP, Nosram and Novak offer a budget range of brushless speedo's. The nosram system is called the Evil, and the Evil Power if i remember correctly. These are pretty much fit and forget, with limited setup options. that said, they have a near automatic setup.
There are some 2nd hand bargains to be had too. decent speedo's are around £80-110. LRP and Nosram are a good option, as are Novak. an LRP Sphere, Nosram Matrix, or Novak GTB would be a wise choice if looking 2nd hand.
Motor choice is good too. Again, there is a budget range of Nosram and LRP motors. The nosram used to be the dragon range, not sure if this is still the case. a 13.5T motor would be a good starting point. It is worth getting a speedo that can handle down to maybe an 8.5T brushless motor however, as it is inevitable that you will want to upgrade in the future.
As I don't really understand bashing, I'd also pop along to your local racetrack.
