Fastest= build a Locost 7 or triple rotor Bugeye
For best all around everyday depends on your needs i.e. 4 dr, awd, fwd, rwd.
You might bee looking for a b5 S4 Audi w/ GIAC chip if you want to stay under $10k. Or look for a built civic or they are cheap to build. If you want something cheaper to track (rwd and stick) go with an E-30 BMW, Miata, MR2. Then there's always the F-body GM cars. Figure out what characteristics you like first then you can find an answer.
For a first car; unless you have spent a lot of time in go karts I suggest something FF with a real double wishbone suspension. Try a honda prelude or something else that is nearly impossible to spin.
On the other hand if you have been karting or racing for years then yea the MR2 will teach you quite a bit. Dont listen to what the boards say about them being reliable though. Its an old sports car and 99% of em out there have been screwed with.
My vote is for an MX5. Cheap, good on gas, and fairly forgiving. Plus they are so slow you have to learn how to actually drive fast rather than rely on the engine.
Just get a 1000cc sport bike. They make great first bikes. Plus, the only person you will kill is yourself (likely during the first week of ownership), instead of the family of 4 that you will probably kill in your $10k supercar.
if you want something to race, start going to races and see what pops for sale there. Somebody will selling a miata or something for a lot less than they have into it because they are moving on and want to dump it, lost their job, got married, or something else. You can always get something already done cheaper than it is to start putting all those new parts on yourself.
For autocrossing, the important thing is buying a competitive car that can be easily set up, has a good class to run it, and does not look like it will be outclassed any time soon.
That my friend is 91-95 naturally aspirated Toyota MR-2 in E-Stock. Find one that is not too molested. Check tranny synchros when shifting. Best is a 1993 and newer, but 94 and 95 are hard to find. Best is a hardtop, but a sunroof is okay too. Heck, the T-tops is not really going to stop you from winning.
There is one for sale on these forums for $2500. A very good one!
Add in a swaybar and shocks, an extra set of wheels, Hoosiers, alignment. Freshen everything up. For about $3000 in set up, you have what it takes to win nationally. Use the left over $4500 from your budget for a driving school, gas, seat time, tire trailer to pull behind it.
Now work on your driving. Not fast enough? I used to put down times in mine that were close to the fastest stock car class times. You will learn to carry speed.
MR2's are great for autox if you keep it in estock. When you have to run in CSP or SM2 well it gets outclassed very quickly by much faster cars like evo's and sti's. But I still autox my MR2 turbo in SM2 and do very well even after buying a lotus.