Disclaimer: In my opinion, there is no reason (barring obvious exceptions such as if you are a racecar driver, food-truck owner, or chauffeur for a large bowling team composed entirely of rowdy German Shepherds) someone mechanically-inclined should ever need to spend more than say $3000-4000 on a car (max), and say $7000-8000 if you're not mechanically-inclined. Those are maximums. My two-vehicle fleet has a combined value of less than two grand, both have more than 150,000 miles on them, and they have plenty of life left in them.
My advice would be to lower your budget, and pay cash up front without any games. Don't buy from a dealer if you can manage it. Get something that will last a long time, do your best to make it last a long time (scheduled maintenance), and then drive it until the wheels fall off (then put them back on and keep driving it).