As a gym owner and software as a service provider, I have dealt across the board with merchant providers. The only advise that I would tell you would be to go directly to the source (not 3rd party providers) to save you the most. The biggest ones are TSYS, First Data, Elavon, Chase Payment Tech.
If you are currently set up with a bank, see if who ever you reach out to can give you price point comparisons. I know for sure TSYS will.
I wish you the best in your search. It can be quite a process to get things set up, but hopefully, you will only have to do it once.
Best in Health,