Some film developers can be saved, mixed back into a large tank, maintained with replenisher, etc. but I think that's too much hoopla for an individual. I discard film and paper developer after each use. For film that's just two rolls of film. For paper you can get about 25 - 30 8x10's from a tray of Dektol (which I use diluted 1:2)(posted 8390 days ago)Stop bath and fixer can be saved. You should test your fixer after each session (there's a little bottle of fixer test chemical that will last about your whole life, you only use one drop) and discard fixer as necessary. Kodak recommends a two tray fixer set-up (old fixer in the first tray, newer fixer in the second tray, then the wash). The fixer in the first tray goes bad first, so discard it, make the second tray fixer the new first tray fixer and make a new batch for the second tray.
So, all in all, you have a bottle of developer, a bottle of stop bath, and two bottles of fixer to store.
In a covered tray you can leave stuff overnight, but it oxidizes and its life is shortened. I put all the chemicals away after each session.
Kodak has a good book about setting up your own home darkroom. There are lots of others just as good. Once you set something up and start using it you'll do your own fine-tuning.