I run a custom, private, appointment-only shop. I do free consult appointments where the client shows up and we discuss the tattoo they want. I take notes, sometimes do little sketches, and then ask if they want to proceed with having me draw up a design. If they do, I collect a design fee from them. I also ask about the size and placement and then try to give a ballpark estimate on time since my shop rate is hourly.
After that I start sketching in the evenings, and when I have something decent I send it over to see what they think. Usually there is some feedback and I incorporate into the new sketches. Once I feel the direction is solid, I'll take the design to completion and send it over. If they haven't set an appointment, they usually do at that point.
Tips are always appreciated, but I have never wanted people to feel pressured into tipping after spending a few hundred dollars. I am in a pretty small town so maybe the protocol is different. I don't do deposits because I find them to be a hassle. Or maybe I'm just a pushover. But in the end it all comes down to keeping the bills paid, and so far that has been working for me.