I'm trying to keep my inventory clear of things I can't use, but sometimes it's hard to tell what items I might need soon vs items I can't use until much later.

I'm pretty sure I'll need wood, stone,.and clay to add buildings to my manor, but I have no idea if or when I'll ever need a magic bomb.

Magic bombs are used for catching wild pets. I don't believe there is a guide on what every item is used for except for the "List of Recipes" under the "Help" tab, which will show you what materials you need to craft different buildings.

Feel free to ask if you don't know or can't find an item's use!

how do you use the magic bomb?

It needs to be in your inventory for you to hire a Magic Catcher (on  the Capture a Wild Pet page), which costs 5 GOLD (not silver).

I can't really remember how to capture a wild pet though. I usually buy GP 3 pets off the Pet Trades instead, even ones with not-so-good genes are easier to start with than a GP 0 pet with good genes.