Li-poly batteries cost $ 1000/kWh and weigh 20 lbs/kWh now for just the cell packs. At even 25C you can draw more power than you can use; 25C means full discharge in 2 1/2 minutes.
Think very carefully about how far and how fast you want to travel. A compact passenger car uses about 20 hp at 65 mph, so you need 15 kWh to run it for a full hour. That's a heavy (300 lbs), expensive ($15,000) battery. Cut the power requirement to 10 hp and you cut $7500 out of the battery cost; same goes for cutting the range by half. Regenerative braking helps in town if you have front-wheel-drive and can engage it before the normal brakes come in. Burst power is free aside from motor and wire weight; at 25C a 15 kWh battery gives 375 kW (500 hp).
You will need a battery management system; Lithiumate builds an OK one but I bet the designers never figured on drawing 200A/cell on a 105-degree day out in the Texas sun, so it let a couple cells cook. You will also have to think of a good way to charge it and keep it cool during charging. The Lithiumate BMS costs around $2000 and the chargers aren't terribly cheap or expensive.
You will want to design the cell mounting carefully. Think about how far the heat and burning liquid from a burst and burning cell travels; can you keep it from lighting off the other cells? If the battery burns, is it a large enough fraction of the car value that you may as well let it torch the rest of the car?
Avoid Kelly controllers like the plague. We have put blood, sweat, and tears into them and they have let us down every time. The throttle response is the pits and they never let full power to be really used. They're made in China and consequently many weeks away anyway. If you use a brushed motor there are many options.
Don't be afraid of high voltages as a designer; it cuts down on the heat you have to dissipate, and most of the components are already rated for more voltage than you'll be dealing with. Do be afraid of high voltages as a car builder or mechanic, as it gets dead-before-you-hit-the-floor dangerous.
The last three Formula Hybrid seasons have been won using a Perm-132 electric motor; about 30 lbs, about 35 peak horsepower. That may be mostly because Texas A&M and Politecnico di Torino used them, though.