Hi Runhappy, I hope I can offer some advice and encouragement. I'm a lifelong car nut and DIY mechanic which may seem counter to Mustachianism but my frugality has always held my wallet in check.
Based on my experience in buying used, I recommend a prepurchase inspection. There are people who are "mobile inspectors" meaning they will meet you where you need them. That will depend on your geographic location but they are pretty common. You may be able to find one on Yelp or other such websites.
I've had better luck buying from private sellers. I've typically seen much better records that they tend to keep in their glove box. I've seen where dealer employees threw out old records as they cleaned the car for sale.
$10k is a good sized budget IMO. I don't know what size and brands you're partial to but if you liked the Lexus, a Toyota would suit your tastes and budget well. Plus, with Camrys and Corollas so plentiful due to production numbers you should have a big selection with many different price points.
Finally, an out of the blue recommendation. I believe everyone is much more mechanically capable than they give themselves credit for, certainly able to learn more than they think they can. While I would still recommend a PPI from a mobile inspector or indie mechanic, IF you decided in advance on a particular model, you could purchase the repair manual for it in advance and commit to learning one simple thing like an oil change. Or, I bet there is a YouTube video for it. One small victory under your belt like that dispels much of the mystery under the hood of a car. Which in turn reduces the intimidation you may feel around the whole car process.