Yep.
I have dozens. None intended to please anyone but me.
ETA: as far as advice; pay attention to aftercare instructions. My oldest tattoo (30 years) is barely distinguishable from the work I had done a year ago, because of how I care for my skin.
For my first three, I had a ten-minute chat with the artist over a basic photo of what I wanted; they made notes on the changes I wanted and booked my appointment. I came back, approved the design, and got it done. Paid for the whole thing at the appointment.
For the next two (different artist in different state) I had a 10 minute chat with the artist over a basic photo of what I wanted; they made notes on the changes I wanted and booked my appointment, and I paid a $50 non-refundable deposit to hold my appointment time. The deposit was deducted from the price of the tattoo, so on a $400 tattoo I paid $50 up front and $350 when we were done, plus tip.
Please remember to tip your artist. 
ETA: they did a terrific job recreating what I wanted; one of mine in particular has a specific intersection included as background, and anyone familiar with the area would recognize it even though it doesn’t have street signs.
No tattoos, but as a person who is an artist, the one thing that I’ll suggest is that you think about your tattoo beyond, “Oh, I like this art piece and, look, I have some easily accessible flesh right here!”
Imagine taking a blank piece of paper and doodling at no particular angle onto it at some arbitrary location.
Now, maybe the doodle is beautiful.
But you look at it and it’s just sort of randomly at an angle, not landscape not portrait. It’s just sort of taking over a random section of the paper, doesn’t fill it and, based on the placement, doesn’t balance out in any way.
Despite being a beautiful little doodle, it’s still a doodle and not a full piece of artwork, because there’s more to artwork than being able to create an image you want. There are still issues of placement, rotation, size, dealing with empty space, etc.
Instead of thinking about it as a beautiful drawing of an iceberg, think of it like a giant Gorbachev style birthmark. Not something beautiful. Just a big ugly blotch. But you get free choice of where to put it on your body so that it’s as aesthetically pleasing as possible. Where would you put it?
Remember the maxim: good tattoos aren’t cheap and cheap tattoos aren’t good. Be willing to walk away if the design isn’t EXACTLY what you want it to be on paper. Have them put a transfer onto you and live with just the temporary tattoo for a while.
Get second opinions. Find an artist who’s art you really love. You only get one shot at this, so don’t cave in or compromise. It’s your body.
Other than that, make sure the parlor is up to code on health stuff, and you will be fine. It sounds like you know what you want. As long as the artist understands you you will have a good tattoo.