Congratulations on getting debt free, that's huge. Your second question is very existential, and only you can truly answer it. Let's focus on the first for now.
Car buying philosophy is a tricky thing, but there are a few rules I like to live by. First, $3-4K is plenty of money to find a very reliable vehicle, though obviously you will have more options in the $8-9K price range. I wouldn't set my budget much below that. At ~$3000 and below, it becomes tough to separate the beaters from the gems unless you have a lot of time and knowledge. Whether you need to spend more really depends on your other requirements for the car (size, type, features, etc). A few ground rules:
- With the abundance of Certified Pre-Owned (CPO) vehicles and transferable factory warranties on the market, I really don't see any situation where you'd want to buy new. Cars depreciate at least 2X as much in year 0-1 as they do in any year thereafter.
- Keep in mind that buying a car still under warranty (CPO or original) is essentially buying a car with an insurance policy. You're paying a premium to reduce your risk exposure if something happens. There's nothing inherently wrong with this, but odds are you'll spend more money in the long run.
- Mileage is a catch-all when shopping used. There's only so much that can go wrong with a car with 50K miles, even if it wasn't well cared for. However, it's not the only factor, and can often take a backseat to evidence of solid maintenance and a conscientious owner. I would happily pay more for a one-owner car with 120K miles and meticulous service records vs. an identical model with 60K, but on its 3rd owner and with a dubious history.
- Milspecstache's point about DIY maintenance is excellent. It will almost always save you money. I enjoy such work, which makes it easier, but even if you don't, it makes financial sense. At $100 per hour of labor at your average mechanic, the added value is far above your current wage and most other things you could do with your time.
My recommendation would be to find several cars you like that have good historical reliability, then move back and forth in the model year range to find years that are in your price range. Avoid the first model year of any new generation (lots of untested design = more things break... hm, wasn't 2005 the first year of the Cobalt?). Then aggressively seek the lowest mileage you can find that has good ownership history.
For example, one of my first cars was a 1991 Acura Legend. It cost $4k in 2002, with ~80K miles. It was essentially a re-badged Honda, but came with all the bells and whistles - V6, leather seats, power everything. Hell, it would compare favorably with most new cars under $30K today. That thing ran like a top for 6 years, with me touching nothing besides oil, brakes, and belts. Perhaps the only "non-Mustachian" thing about it was the 26 highway MPG (still pretty decent by today's standards), and I could have gone with the 4 cylinder Acura Integra if I so chose. You can find numerous examples of Nissans/Hondas/Toyotas or their equivalent luxury brands that would serve a similar role today.
Bottom line? Both of your scenarios are feasible, but spend enough to be comfortable with your purchase. Even if that's the more expensive option right now, take the time to learn about your car so that next round, you can save the extra $4-5K.