> It seems like you have to get lucky or do a lot of research. Or both.
Yep, no question here. While Linux compatibility has gotten a lot better in recent years, you're definitely rolling the dice a bit in driver-land if you don't research beforehand.
That said, since pretty much every big distro is free, it's not necessarily a bad idea to just download it and try it out, at least with a Live USB Ubuntu image or something. If it works out of the box, then maybe you should install it, and if it doesn't, just unplug the flash drive and restart the computer and stick with Windows. It's entirely possible (and even likely these days) that it will Just Work (tm), and that might influence your decision in switching.
> But there's probably no point at which Linux will work well on all hardware
Yes and no; I think Linux tends to do exceptionally well on older hardware. I've been able to breath life into decade-old computers by just installing Linux Mint with MATE desktop [1], and generally by the time a computer is designated as "old", drivers on Linux are often better than they are on Windows, and due to how stupidly customizable Linux has become, you can get extremely lightweight desktops that require basically nothing to run (e.g. LXDE, MATE).
On newer hardware? Eh, as I said, you're rolling the dice a bit. Generally if you stick with AMD hardware, you are fine, as I said, but that's by no means guaranteed, and to me getting WiFi to work out of the box is the scariest thing, since if you cannot get connected to the internet, it's difficult to fix any of the problems.
[1] I did this for my grandmother who is still running an old AMD64 single-core computer. All she uses it for is browsing the web and checking email (not even YouTube) and she refuses to buy a new computer. Linux Mint has been a godsend.