your question is a really wide ranging one, to be honest, because "hardbound classics" could mean a lot of things.

I would start by asking you about budget. Let's not worry about the options out there for collecting, because there are too many. Rather, consider what your budget is, and start there, because you will quickly find things in he price range, and then you can determine if they are what you are looking for.

There aren't going to be any $50 first editions in great shape, or really well done editions.

But as someone mentioned, The Barnes and Noble editions would be a great thing on a kid's shelf maybe. You can get Easton and Franklin Library stuff on eBay pretty readily...

for the most part, books made to be "collectible" (Easton Press, Franklin Library, etc.) are really readily available and can be had fairly affordably. They look snazzy, and appear to be fine bindings but in reality they are much more affordable modern reprints. When someone makes a million of something and calls it "collectible", you have to take it with a grain of salt. These will look nice, not cost too much, and be appreciated. They won't be heirloom quality or 'investments' though, despite much wishful thinking by their admirers.

The Folio Society makes more well-considered (IMNSHO) editions, in cloth usually, with new academic commentary, illustrations, etc. These are usually quite nice, visually. But they can be a hundred to a couple hundred bucks. They are also marketed as "collectible", but I think they are more honest books. They aren't pretending to be anything they aren't (e.g. no claims of "fine leather bindings", which some others make).

Aside from that, you CAN find great older copies, not necessarily firsts, for decent prices. try vialibri.net for starters. This takes education (about what you're seeking, I mean) and time. Many people don't have the knowledge or time for cruising the net looking for underpriced gems. But they are out there.

first editions? fine bindings? children's literature ('Black Beauty', etc.)? classic literature?

True first editions can be prohibitively expensive. And even children's books are quite highly collected. Good copies of the classics will be costly. But they have the greatest potential to rise in value (to preserve the money spent on them, at least). There is a certain logic to buying a true first edition, and paying the premium, because it will typically appreciate in value. Though don't plan on it. Don't make that false claim to yourself that it's an "investment". Some books are, but when you pay retail prices from a dealer, it will take you a while to regain the full value spent.