Those who pretend you need to spend $1K or get a used bike formerly worth $1k new are delusional.
There is very little benefit between a $400 bike and $1K besides the weight difference, if you shop wisely.
What you should look for buying used off craigslist or any local avenue, is that the bike is adjusted properly and operates smoothly so you don't need to pay a bike shop (if you can't DIY which you probably can't without a learning curve after so long without riding) to get it adjusted well. If you want to tackle that learning curve, GREAT, it will benefit you in the long run, but I should back up and mention that buying used meant a major brand, which doesn't have to be some $1K MSRP bike, just something main brand with recognizable components.
It does not need to be single speed or any other niche idea that someone else considers nirvana. It just needs to be solid major brand with major brand components, that is either adjusted right and ready to use, or priced low enough that paying someone or DIY is reasonable for what you're getting.
As far as what to look out for, it is fairly straightforward. You know you need tread on your tires so if they are worn out, or cracking from dryrot, add that expense, or I should write deduct it from the value. Grips that are worn, are another small expense. Gears sprockets with worth away teeth or a rusty chain or one with much slack in each link is also a little more expense to nickle and dime you, and yet it is not unreasonable to expect to spend a little money to get a used bike back to good shape and will still save a lot of money over buying an equivalent bike new. You know what unworn components look like, and any that are worn, may need replaced soon. Anything can be replaced, unlike a motor vehicle this is not a make or break deal depending on small parts unless the frame itself is substantially damaged. Even then, some people buy new frames but I digress, this is not a starting-over thing to do. The point is that a major brand, median quality bike is modular and can have any components replaced with same or upgraded parts depending on your needs and budget.
"proper fit" has nothing at all to do with how much money you spend. Do go to a local bike shop and try a few on for size, and do pass on any bikes used you find wherever, that don't feel quite right.
Like anything else, there are the two extremes that you should avoid at this point, off/no-name department store bikes, and overpriced luxury bikes in the $700+ price range. Get a median priced used bike then go from there deciding what more you need if anything.
Remember that if you get a major brand using standardized components, you can upgrade individual components as you see the need or from failures, do not need to spend top dollar for overkill everything just to ride some paved bike paths. That is not at all the same scenario as a road biker putting on several tens of thousands of mi/yr or a MTB rider who needs to survive doing jumps. Or just look kewl to his peers.
In any case, budget for a good helmet and lighting if riding after dusk. You are more valuable than the bike.