What points are you confused about?
I wanna be able to receive bitcoins, i'm not sure if it would be safest to get my own wallet with an app, or use a trusted 3rd party website?
Desktop wallets are your best bet. I personally recommend
Electrum. Setting up a wallet with it is fairly straightforward, as are sending and receiving transactions. Try starting out with a standard non-segwit wallet (because some services do not support payments for segwit wallets), and be sure to set a strong password, and keep your seed words safe and offline. It also has a phone app. You can explore the other features later (like 2FA, Segwit, etc.), once you get the hang of things.
It also has a dedicated subforum
here should you ever need help/support.