You can absolutely do that. If you want to upgrade to a paid plan to get some of the features you want, then you can switch at any time through the My Products option in your account or with the help of a GoDaddy Guide. Once you upgrade your site will have all the same customizations and work that you've already put in place, just with the added features. See Website Builder plans and pricing for more info.
If the owner has agreed to sell the domain, try to get the agreement in writing if possible. Or better, draft and sign a purchase agreement with the buyer. This will legally dictate the terms of the purchase and protect both parties. Next step, you’ll have to make the payment. Don’t just wire money to the buyer once you have reached an agreement. You need a secure transaction to protect you from any fraud activities. Use a secure service such as Escrow.com to close the deal.
Choosing a domain name isn’t easy. You want a website address that will be both memorable and meaningful while simultaneously describing what your brand is all about. But even after you’ve come up with something catchy and worthy of your brand, you may find that the .com domain is already taken. That only leads you back to the drawing board, which means more headaches.
But…there are times when you are simply not satisfied with the selection of domain names that are available to register at a minimal fee by yourself. Sure, you could always register your domain name on a .net (less popular than a .com but still widely used) and maybe even a .org (good if you are a non-profit business, church, NGO, etc) but if you have a little more funds to spend than $10 a year, then your next best thing is to go ahead and buy a domain name that you like from a domain seller or from a domain marketplace.
8 Rules for Choosing a Domain Name - Whiteboard Friday