best low $ auto-reverse cassette decks?

I'm not really an audiophile, I don't have the money to really geek out. Just want to know what I should look for in the lower end of equipment that still sounds good. Just picked up Fischer studio standard amp, tuner, and equalizer (and broken tape deck) for $25 if that tells you anything.
What's a Cassette?
I like cassette decks but I don't trust auto-reverse mechanisms. Especially if they're cheap. Tape playback quality ( and recording but that's another issue ) depends so much on proper physical alignment of the tape with the heads that it seems nuts to build in a gadget that will invariably tend to throw the alignment out.

That said, I would consider a Nak 202 or 505, or that Uher portable which was not much bigger than a paperback--such elegance. But they're not low $. So sorry, this is not an answer to your question, it's a suggestion that your question may be an oxymoron like "jumbo shrimp".
Denon used to make some fairly decent inexpensive decks. Check out for one of those used. I have a Denon DRW 840 dual well deck I bought in the mid 90's and am quite happy with it. My only complaints are that it's not a three head deck and that the wells aren't backlit - that would have been a nice touch. Spend as much as you can afford if you have a large tape collection as it will pay you back over time by not eating your tapes plus you'll have better sound to boot.

Good one bug.
I had a dual deck Yamaha that did all sorts of auto-reverse, I think it had three or four different settings. Also had headphone jack. I sold it for $40 about six months ago. I think it was a CDC-755 or something like that. Maybe a 655?? Anyway, was built great and sounded the same. So, I would look into older Yamaha models.