Well tyre wise best place to start is Schumacher Yellow Minispikes. They are pretty much the standard tyre, and work well outdoors at Goshen when new, and indoors at Chadderton when worn. They are however pretty hopeless in the wet.
For wet weather most people use either Schumacher green minispikes or Ballistic Buggy green spikes.
Battery wise a single decent lipo is all you'll need. Something in the 4000mAh+ range and 25C or better discharge rating.
These are quite good value for money