In my less than professional opinion, I'd get a list of artists that people have recommended to you & then just start cruising their Instagram, get a feel for what their styles are like & then pick the one you feel fits your tattoo plan the best. Most tattoo artists nowadays are very active posting their work on Instagram, far more than on Facebook or their shop websites Make up your own mind about who's art you like. Do you have images of what you want done, like pics of the characters and the poses you want them in?
As far as getting the work done in sessions, how big a piece are you looking to get? Where do you want it? What's your pain tolerance? I personally like getting it all done in one sitting, I like having the finished product right then, but it's more painful. For bigger pieces getting the outline done and then colour fills later is pretty common.
Getting your first tattoo is the hardest. I drew mine and had it around for over a year and a half, showing it & telling people I was going to get it done real soon. It wasn't until someone gave it to me as a gift that I actually bit the bullet. It can take time though to fully realize what you want & what's important to you in life that you want to permanently represent it on your body. I have 7 done over the course of 9 years, but 6 of them have come in the past 2 years.