If you are serious about racing... especially auto cross, rally, or road racing you will become more competitive if you spend most of your money on racing school instead of the latest greatest equipment.
That said......in auto cross the cooper mini is dominant in its stock class, the cooper mini s is strong in its class. The miatas and solstices/skys are epic and will have tons of info to research on forums. All good cars to consider. At first stick to stock classes and never go cheap on tires... After that all you have to do is practice and learn.
Good luck..... and race safe