Awesome that you’re interested in ham radio!
What can I (legally) do with this thing without a license?
Listen, mostly. Baofeng radios are typically sold as “Part 97” radios (FCC lingo for “Ham use only and requiring a license”), although there are some models which are actually “Part 95” which would be GMRS/FRS radios. The GMRS/FRS radio model would require a separate license for GMRS, although that one is essentially an application + fee payment. It’s also not nearly as broad as a amateur (ham) license.
Edit: I forgot that the Baofeng radios can also transmit on frequency ranges that are technically outside of the legal ham/GMRS allowed frequencies, like business communications, police/fire, etc. Be warned that even with a ham license there will be some things you aren’t legally allowed to do with this device. It’s definately not a toy.
Any pointers for learning the basics on this particular machine?
Again, it will depend on the model, but personally I find the Baofeng/Chinese model radios a giant PITA to use. They’re cheap, sure, but aside from using the programming cable they can be much more difficult to program/use as compared to the Japanese models like Yaesu or Icom.
I should read the manual cover to cover, right?
Sure, I suppose. :)
Looks like it’s easier to program from a computer, any tips on that?
I can highly recommend CHRIP as good programming software. It’s also open-source: https://chirp.danplanet.com/