Steam's built-in backup is an option, but it's about 50/50. Some people think it's the best thing since sliced bread, others would like to slice it up as if it were bread. Personally I tried once and it failed and I went manual after that.
Another option is "manual" backup and restore but it would be best with a script -- manually moving save files (which may not go into the same exact spot on Windows because of different paths across versions...lol) is not really fun. There's also the problem of not all saves being in the same folders as there's no real standard unless they're using Steam Cloud...in which case you don't have to care unless you're extremely worried about losing the game save.
On Windows, GameSave-Manager is an option for automation but it doesn't support all games by default. Do not use Link & Sync unless you're confident in your nerd skills as it will setup junctions/symbolic links that can screw your games up bad up if any part is improperly removed.
On all systems you can manually find saves at the paths listed on PCGamingWiki, but it doesn't have all games data listed though they're trying.
Steam/steamapps
folder will contain your installed apps (in the /common
folder) and their manifest files (necessary for the client to easily recognize that they're installed). External Library Folders will have their own steamapps
folders that need to also be copied, but you can merge them all together. Steam/userdata/{youruniqueuserid}
contains files that are synched with Steam Cloud including game saves, but some can be destroyed by a fresh install. /7/remote/sharedconfig.vdf
in particular contains your "categories" and is a tragic loss if you've manually built one.