You and I are almost in the same boat. Coinbase seemed much simpler & less complicated, didn't it? Anyway from the brief understanding I got is roughly this...
Purchase your bitcoin through the exchange of your choice, Coinbase, ChangeNow, etc. However, instead of storing them with the exchange, transfer them to a personal wallet like Electrum once you've downloaded it. (Yes you need to download it though)

This is the point I'm at now. I've downloaded Electrum, transferred some bitcoin into it from my exchange. Now I currently testing it by sending a small about to another wallet. I should know within a couple hours if it worked.

I have a few more questions that I can list that might get more answers & hopefully help us both maybe.

1. Does it matter weather or not we leave our wallets from Electrum open after downloading, or should they remain closed when not in use?

2. I know it recommends storing Electrum on another device not connecting on-line...But until I'm able to get another device to put in on, is it still ok to use going on and off line?

3. Lastly, if I'm sending bitcoin to an onion site through (tor) instead, should I or do I need to do anything differently?


Well I realize I may not be much help, but hopefully we might both learn somethings because of it I hope.