... I don’t want to go into this too cheap and screw myself over.
I have news for you. If this is your first one, that is unavoidable. It just is. It takes time and a lot of experience in custom painting to become any good at estimating time and materials. Underestimating the first time is just something that is going to happen. This is not even so much about the painting time and material use, which you probably have a good handle on when working on your own stuff. It's the creative chaos that comes from learning to work a customer, rather than work a brush.
Customers are all over the place, keep trying to change things, commit to stuff, then back out, delay you on reference material (if say they want a you to do their kids, pet or beloved partner ), wiffle waffle on decisions, etc. That is just a normal part of dealing with the hot mess that is a human being. It's not a bad thing, but it takes some getting to grips with and learning how to gently steer them and their decisions toward something that they actually want (not just what they say they do) and that is actually accomplish-able before the sun burns out.
What I will suggest is you take your time and materials price that, then triple it. Trust me, you are gonna eat a whole lotta time on back and forth and redos the first time out. Also, for a first time client, take a minimum 30% non refundable materials/layout deposit. Then if it all goes wrong, at least you aren't blowing through unrecoverable materials such as paint, frisket, wear and tear on equipment, etc. It also acts as a bit of a bozo filter. If they can't come up with 30% up front, they aren't gonna be able to come up with the rest down the road. I had lots of pieces abandoned over the first few years because people walk away from the project. They get an unexpected bill, or delayed pay, or kids need braces, or abducted by aliens... whatever the reason. So you get left with half finished stuff. They can't pay, and then either ghost you, OR come back wanting a piece or a part they left with you, but not wanting to pay.
Make sure you have an abandonment or non-pay provision in your contract that the ownership of the part remains yours until the account it settled, and deadlines for payment after project completion.
Also, your first few times you are gonna go over and above. You won't have the routine in place that makes you fast and accurate, that comes with time. So you'll be unhappy with things, keep reworking them, etc. What the customer thinks is amazing you won't be quite happy with, so you are very, very likely to keep working long after the project would be done by anyone else's standards. Experience tames this instinct, but it will bite you hard when starting out.
Know that you are going to under estimate your first few times, and be OK with that. Just make sure that your materials are covered up front, and then have some fun getting to know your speed and style. By the time you have done 3 or 4 custom works, you will start to have a really good sense of the scope of work, and how long it will take you, and what kinds of work take the most and least time.
It is exciting doing custom work, and you'll love it, just be prepared for a bit of a learning curve dealing with customers and setting their expectations and scope of work.