I would combine this with the Custom Wizard plugin. Using that plugin you can capture any/all information you want on signup and then when the form is submitted, send the user to the membership payment page. That way you have it all in one flow.
Personally, I prefer it this way as opposed to the Paid Memberships Pro route. PMPro can work great up until you start trying to sync group memberships back and forth. You can do it, but in my experience it’s not as easy to set up and isn’t always reliable.