Death Track: Resurrection

This one is very easy: in the single-player menu, at the bottom, there's a button called "Customize Car". You can buy a new car, buy upgrades and weapons for your current car. Be careful, though, weapons and upgrades do not carry over if you buy another vehicle (you'll need to buy them twice).

You should start with $50,000. Buy a car first (you'll get Test Drive), if you don't have enough money, do a race in the scenario. Then equip a new weapon (you'll get Rearming) and buy an upgrade (you'll obtain Mechanic). I advise taking the engine upgrade, it clearly boosts the power of the car and produces amazing results in races.