Picking out melodies by ear is an excellent practice that should be developed by all players. Once you have learned to read tab, you can check how well you did.
It is normal to have your fingers hurt for the first couple of weeks or so.
A pick or fingers are both ok. Kirk's lessons here are finger picked so you might want to, at some time, consider hybrid picking if you chose to play with a pick. Some people learn to play with fingers and pick too.
It takes about 30 days to make or break a habit so you have time to read through some of the info on this site to get a feel for what to look out for. The only thing at this point, I can think of, that would be relevant for you is to keep your thumb, more or less under the middle of the neck. You will have much more freedom of movement than having your thumb resting on the side of the neck.
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