I have a android, I guess I could put some wallet on there?
Yep you can for sure. There're many(plenty of) clients available for android. I'd entreat you to have a look over here->
https://bitcoin.org/en/choose-your-wallet#android And then transfer to wallet from bt, and in my wallet will I have the data
You mean data=funds(btc)? Yep, you'll surely see the funds(btc) in your android wallet.
I guess that they will want me to hang around, or transfer the money first and wait for confermation (probably 2 or 3 = 15 minutes?)
Basically, you've to read out(go through) their help(guide) section->
https://localbitcoins.com/guides/how-to-sell-bitcoins-online I don't have a lot of btc, but I'd kind of like to get my btc offline
You can go(check out) for bither (offline) wallet there->
https://bitcointalk.org/index.php?topic=498382.0 I always worry about hackers.
Basically, you don't have(need) to worry about 'em as far as you use a strong password & a strong antivirus (IMO).
Electrum seems like a popular brand-any major negatives?
AFAIK,
electrum's a secure & popular wallet for sure (with no major negatives).
I know how to send btc, but only at my computer.
BTW, I'm not sure that why're you looking out for an android wallet (if you do have access to your desktop client/wallet)?