Hi Joel,
Great question! I’m really glad to hear you’re giving our plugins a look for your project. 🙂
I think Event Tickets and Event Tickets Plus would be great to handle tickets for specific museum events, but probably not the best for something like an annual membership. For example, each ticket comes with a barcode that you can use to scan and “check in” a guest — that wouldn’t be so great for annual members who likely would be able to enter the museum a number of times with a single ticket.
That said, I think looking into something like WooCommerce and it’s Subscriptions extension could be an interesting thing for you.
Sorry for the bad news on our plugins, but I do hope that the other route at least gets the ball rolling in the direction of a much better fit. And, of course, feel free to let me know if you have any other questions and I’d be happy to help as best I can.
Cheers!
Geoff