My wireless company is Consumer Cellular. I currently have a Samsung S9 phone. I'm planning on buying the iPhone 15 Pro Max. Should I expect to have any problems with setups and transfers?

You shouldn't have any problems.

When I switched to my iPhone 14 Pro, all I had to do was call CC and ask for tech support. They ask for the IMEI of the phone so they know whose eSIM to activate. After that, it only takes a moment or two for the switch to happen. The new phone will be the one to respond to the cellular system, and the previous phone stops.