The car that has the most potential is, to be honest, the car belonging to the guy with the most skill at building.
Look at the Grassroots Motorsports $2004 challenge. This is an event where the contestants have to build a car under that dollar figure (which goes up by a dollar each year...) including the cost of the car, and everything has to be fair market value; i.e. anyone could have reasonably gotten the same deals. The cars have to compete in a drag race, an autocross, and a concourse (car show).
This year, there were at least 5 cars running 11 second quarter miles, and one that ran a 10 second quarter mile. There were cars that did both drag racing and autocrossing very well.
And the kinds of cars that showed up?
There were a couple Neons, a bunch of V8 RX7s, a few CRXs, a few Mustangs, a couple V8 Datsun Z cars, a couple Miatas, a Porsche 944 and a 924 (with a GM V6), an AWD turbo DSM, and more (there was an early VW bus, cut down, with a mid engine V8, and the CRX I posted in another thread that was converted to RWD, with a small block Chevy V8...).
Last year's overall winner was a Ford V8 powered Miata that was indeed built for a grand total of $2003. 12 second quarter miles and incredible grip and handling, and looked good, too.
Now imagine ANY of these cars with an extra 8 grand to spend to come up to your $10k total budget...
The point of all this? There IS no "best car." only what YOU can come up with that you like and create. My personal choice?
Well, the BMW in my sig was originally going to be a $2004 challenge car, but I decided that the wheels I wanted would use up most of the budget, so i decided not to compete. But it would still end up costing me far less than your budget (the engine I decided on can now go over the $2004 total budget, which allows me to get aluminum heads to make closer to 650 hp for under $2500 for the whole engine...). But I also love V8 powered RX7s, either a light early RX7 with Miata IRS, or a slightly heavier 2nd gen RX7 with it's stock suspension, like the one i already built.
This car ran 12.1 in the quarter, pulled 1.2 G laterally, and cost a total of under $3500, not including the original car (which I already had, but I could find for under $500 these days...):
And for the people that don't like that, now, 10 years after I built that car, similar power levels can be made from turbo rotaries (though still not quite as reliable) and still keep your total budget well under that $10k level.