I would build you a completely custom system from scratch. It would be designed to run completely stable, fast, and efficiently with the best practices in mind. What I would do is create a foundation written in Golang that can be expanded on and allow an API at a later date if you wanted to do that.
For payments it would be up to you on what processor you wanted to use. Paypal and Stripe are pretty popular. We can have a full user system with admins, moderators, and a full tiered paid membership system. I'm a gamer as well so I have some experience in that area of what people are looking for.
I would love the opportunity to work on this project with you and I'm confident I can build you exactly what you're looking for. If you have any questions or want to see more of my qualifications that aren't in my profile please feel free to send me a message.
P.S I would use Go over PHP as I have much more experience with it. It's faster, compiled, and will run natively on just about any operating system without needing any requirements or libraries installed.