I see. Depending on what payment processor you need to use, you could be better off simply paying someone to build the integration. There are one or two people here who do such work.
If you still want to do it your way, then this is what I’d do. Take the payments as you suggest, and also take any other details at the same time that you want them to have on the WP site. This means that they won’t have to register again. Then use either s2Member Pro’s API or WP’s own REST API to send the details of each registration to the WP site. These details should include the level or ccap that you are assigning to them.
After successful payment, I would redirect each new member to the password reset page on the WP site so that they can then enter their email address and have the password-setting instructions emailed to them. Then they will be able to login.
You will, of course, also need to figure out how to handle renewals.
There is, however, a third way that you could use if your payment processor is supported by WooCommerce. Then you could use the WooCommerce Role-O-Matic plugin to enable people to sign up directly on the WP site and be given an s2Member role. WooCommerce Role-O-Matic should also be able to handle renewals. I don’t know if there’s a way to automatically login someone after purchase, but WooCommerce has plenty of hooks so I would guess that it is.