I have a 2016 Mongoose Brawler that I am fixing, among the things that need to be replaced, the rims are one of them. I have 16" tires, so what size rims will fit those tires? And then what spokes size will I need to fit the rims?
If you are not an experienced mechanic and if you don't have wheelbuilding tools, this is something that's probably best left to the folks at your bike store. They will have the tools to measure the effective rim diameter (ERD) and the relevant hub parameters (i.e. center of hub to center of each flange, noting that this is symmetrical in front and asymmetric in the rear, and the flange diameters).
Often, rim manufacturers publish ERDs on their websites, or the ERDs may be floating around in Excel files for wheelbuilders. The same is true for hub measurements. My understanding is that mechanics will still prefer to measure those parameters themselves, because there may be some ambiguity in how people define each measure, or the rim or hub model wasn't in the database or it received a running manufacturing change. I was under the impression that ordering spokes 1-2mm too long (but not too short) is still acceptable for a wheel build, so there could be some room for error in the measurements if you're taking them yourself.
If you are determined to take the measurements yourself, I'd consult this Park Tool page. It should either give you what you need or convince you to outsource the task to someone with experience. If you are determined to build the wheels yourself, you could consider if you can pay a mechanic at the bike store to measure your hubs, select a rim, and order spokes for you.