Second, if it looks interesting but you’re not quite ready to commit, ask your library to get it. Most libraries have digital options, and many are part of consortiums that have bigger purchasing power than you might think. And I’ve never met a group of people more excited to get requests than librarians. Now onto format specific recommendations.
You should check out a streaming service if you’re planning to race through a huge backlog of books. I’m doing a Claremont-era X-Book run now, and it’s so much easier being able to bring 35 issues on a plane on an ipad than it is to bring a trade or an omnibus. I have LOTS of recommendations for what to stream at Marvel Unlimited and DC Infinite if that’s what’s holding you back.
You should pre-order single issues if you like a creative team and want to keep seeing their take on a character, or if it’s creator-owned or from a small press. There will always be a comic called X-Men or Green Lantern on shelves, but your favorite artist’s run might get cut short if the book doesn’t sell well upfront—see Omega Men in 2016.
You should chase down back issues if you like the thrill of the hunt, you can spot a key issue at 60 paces, or you can’t find a copy anywhere else. It took 10 years before I fully read Abnett & Lanning’s Legion Lost, and it took another few years before I had gathered most of their full run in singles, so that when DC finally started collecting their work in trade, inertia made me complete the set. But that was actually a lot of fun! And I find a certain collector’s wanderlust pushing me to start thinking about other runs, too. If you get that feeling, hit those back issue bins at your local comic shop!
You should get trade paperback collections if you like a story, want a more compact way to collect physical copies, and want it now. Trades look really nice on bookshelves, and they provide immediate reading material that is (usually) certain to be printed through to the end, which you can’t always say for larger formats.
You should buy compendiums if you don’t trust streaming services entirely and you want to own something you’re going to read to death. These books—DC calls them compendiums, Marvel has Epic Collections, Dark Horse does library editions, IDW calls them omnis—usually have slightly worse paper quality and less fancy bindings in exchange for a TON of comics. This isn’t universally the case—the Black Hammer Library Editions are as good or better than Marvel’s (slightly more upscale than this) omnibuses, and they’re way cheaper. These are, to me, the best bang for your buck.