Sounds like a good budget but it won't buy a fire breather. Like was said above purchase on bodywork condition alone! Check for rust in all the usual places including the rear valance corners, roof gutters and where the scuttle panel and wings meet, also the front grill surround...basically everywhere.
Ignore all the talk of 10" wheels, they are great but require either original 7" cooper or 7 1/2" Cooper 'S' discs - and they are very expensiveand are not a straight fit as you also will need different drive shafts and outputs.
For an everyday car thats nice go for a good bodied 12" or 13" wheel (with discs- usually 8" IIRC?) running basic car, you can always tune it later! The parts are very cheap for minis but the actual cars are quite expensive.
The 12" will give you lighter steering and the 13" will be a bit heavier, in a mini its not all about grip, but balance....(If it has aftermarket 13" wheels, make sure the offset is right or steering can be very heavy!)
The seats and interior are easy to modify to accomodate a different height of driver, and you will be amazed how comfortable they are.
Basically they are great fun and a fantastic car to hone basic driving skills in, 30MPH never felt so fast!
Above all have fun with it

Good Luck!