Well, first off, if you're talking about the Infinit FX35 - those don't get good gas mileage at all. And they run around $40,000+, depending on options. So you'd be looking at a really used one.
Second, the VW Beetle has a ton of head room. You should check it out if you like it. My boyfriend is 6'6'' and he can fit in one. 5'10'' should not keep you from any car, since most men are around 5'10'', give or take.
Lastly, with a budget of $13,000 (which is pretty high for a first car!) you're not going to be able to find much brand new. Except maybe the Chevy Aveo. Or a Hyundai or Kia. And 20 mpg is not really good gas mileage, actually. I think gas mileage is considered good when you get up around the 30mpg+ range.
Good luck.
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