As to which service to attend, I'd say whichever one is next, and definitely attend the next available Divine Liturgy. No matter how much you read up on it, it will be new to you for a little while, but it will grow on you and you'll soon not need the book to follow along.
You're welcome to participate as much as you want, with the exception of getting in line to receive the Eucharist. There is nothing that is "appropriate" or "inappropriate" for a non-Orthodox to do. The only thing reserved for the faithful during the Liturgy is the Eucharist; everything else is fair game. Feel free to say "Lord, have mercy", "Amen", "To Thee, O Lord", or anything else to your heart's desire... or say nothing at all...
As far as becoming a Catechumen, talk to the priest and tell him what's on your heart. The two of you can then work together toward the path that is best for you and your spiritual situation. It's different for every person depending on their needs and spiritual state.