Wayland has better support for some newer in-demand features, like multiple monitors, very high resolutions, and scaling. It's also carrying less technical debt around, and has more people actively working on it. However, it still has issues with nvidia video cards, and there are still a few pieces of uncommon software that won't work with it.
The only alternative is X. Its main advantage over Wayland is network transparency (essentially it can be its own remote client/server system), which is important for some use cases. And it has no particular issues with nvidia. However, it's essentially in maintenance mode—bugs are patched, but no new features are being added—and the code is old and crufty.
If you want the network transparency, have an nvidia card (for now), or want to use one of the rare pieces of software that doesn't work with Wayland/XWayland, use X. Otherwise, use whatever your distro provides, which is Wayland for most of the large newbie-friendly distros.
My first step is usually to figure out whether the package should exist as a separate entity under Gentoo (which, for instance, doesn't have separate dev packages). Then I check the overlay masterlist to see if there's an unofficial package (which there often is).
If there is no package, I can package it myself (since I've been working with the same distro for years and can handle the basic packaging cases), install from source, get the .deb and apply alien or deb2targz and proceed from there, or give the whole thing up as a bad job.