Going to assume that's not your route, because you're going to be missing out on some of the best parts of the country..
There's some awesome mountain roads and parks in Vermont/New Hampshire, most of Utah/Colorado is amazing for driving, Florida, while it has it's issues, is pretty sweet too, and you're missing tonnes of awesome cities in the south east..
Also, Mustang should be alright, wouldn't be my first choice..
Just a word of warning though, $8000 for car+Trip is kinda low maybe, depending on how you plan on doing it. Assume every hotel is going to cost you $100/night and hope it averages out, gas will cost more than you expect in some places, food, will be very expensive unless you have some way of cooking for yourself while on the road. (Like, EXTREMELY expensive.) You're looking at $10~15 a meal unless you want to risk getting the shits from eating nothing but junkfood the whole trip.
If you're going to camp with a tent/cooking setup, a Mustang should have enough room as long as you pack light, and buying stuff at a grocery store is going to cost a hell of a lot less than fast food/restaurants.
I've taken a few road trips from Maine~Florida~back and Those alone are generally $1200 round trip for just gas/lodging/food.
And one last thing, you will be putting a fuck load of miles on that car, you're going to have to make sure you've got new tires to start out with, and you're going to need atleast one oil change on the road.
Not trying to deter you from going, it'd be a seriously exciting time, but you sound like you've never done something like this, and costs add up so much faster than you will expect. I seriously wouldn't do this in a sub-4-5k car unless I knew how to fix it myself with minimal tools/parts