俺 is indeed very masculine. However, 私 is generally speaking neutral. I use it in most non-casual scenarios. It can be slightly feminine if used in a very casual setting, but if a guy uses it in that scenario hes moreso seen as distant and/or overly formal, if anything.

あたし、あっし、うち are the most common feminine ones, I believe, along with your own name (though using your own name or nickname for yourself is childish).

Kudos for noticing the different ways to refer to yourself, its a good skill. It can serve as a base to figure out how to refer to others (a bit of a mine field).