You do not need to pay for additional hosting, or another domain name. You just create another database and install a second copy of WordPress on your website, either in a subdomain, like members.yoursite.com, or in a subdirectory, like yoursite.com/members, no problem!
You're not going to get that much integration with PayPal, and I wouldn't suggest it anyways, what if you decide to expand beyond PayPal and start accepting credit cards or other forms of payment?
My suggestion would be to use another great plugin called Register Plus. This enhances your registration process with more options, including invitation codes.
So Members Only keeps non-members out, and Register Plus keeps those without an invite from signing up. Then you just sell that invite code through PayPal. Of course you may want to change this invite code periodically if you think it may be exploited.
Or if you are not expecting to sell a huge volume of memberships, you could easily create X amount of invite codes at a time and sell them individually through PayPal, so that everyone has a unique code.
WP e-Commerce has a Member's only module that you can use to sell subscriptions, but it is a commercial module, and I haven't tried it myself so I couldn't tell you if it is any good.