I would get some hardcase lipo batteries. Check the size (especially height, to avoid hitting the belt) but I expect 2S 5000mAh to fit, will give you over an hour on one charge. The ones from which the cables exit on one end of the top plate are better because the way the battery mount is made.
The brushless esc I expect it has lipo cutoff (just make sure it's activated from esc setup), but the lipo alarm certainly does not hurt
Good choice of charger. To avoid stressing the balance connector on the charger, get a 2s balance lead extension and leave it plugged in the charger. Will also ease up hooking the battery to the charger.
We usually solder the connector of choice (for example deans) on battery / esc / charging cable to avoid adapters, but that's for convenience, drifting does not require high amperage so no harm in using adapters, if you're not into soldering.
Get at least two sets of different drift tires, softer and harder (for example mst red dot 101024 and silver dot 101026), and enough rims for all of them. When playing choose the one that feels best depending on surface and temperature.
Practice, practice, practice.