So I kiiiiiiiinda just got a Moto 360 for free.
Yeah.
What should I do with it? Just set it to charge after setting it up to read my phone. Are there apps or things to do with it?
Charge it first before setting it up. Once it's full, then install/update everything.
There's not really much to do in terms of adding apps other than
Wear Mini Launcher, which (for me) isn't really ideal. It actually gets in the way most the time unless I'm looking for a very specific thing.
Google Fit is now available, so download that.
Runtastic is now compatible with Google Fit in that it shares your workout data.
Note-taking apps:
Google Keep or
Evernote.
If you want, you can pin your Google Music tracks to your watch and listen to music via Bluetooth directly from your watch without any phone requirement, but there's a heavy battery penalty in the amount of 1% drain every minute.
There are some watch faces you can download, but the default ones I find are perfectly acceptable for me.
Moto was owned by Google for the whole year until like a month ago. Not surprised if they had access even beyond the Nexus team.
There's been interviews with the Motorola Moto X team stating that for the first gen Moto X, they had to submit a request for access to the new Kit Kat build just as any other OEM. They were treated no differently (if they're to be believed).