Do I need hand wraps if my gloves are padded?

Yes. Gloves protect the person you hit; wraps protect your own hand and wrist. Bag work without wraps is how most beginners injure their knuckles and wrists.

What glove size should I buy?

For general training, 12oz if you are under 150lb, 14oz between 150 and 180lb, 16oz above that. Most clubs require 16oz for sparring regardless of weight.

How do I stop gloves smelling?

Take them out of the bag immediately after training, pull the wraps out, and let both dry fully in open air. Glove deodorisers help; sealing damp gloves in a bag is what causes the problem.