I register copyright on all my novels. I think the deal is if you register online it's $35/$55 and more expensive if you send in paper documents. I believe (this is what I heard, and it seems to have borne out in my case) that it's $35 if you register just with one name, your real name OR your pen name (if you use one), $55 if you register with your real name AND add your pseudonym to the registration. I use a pen name; I've always registered with both my real name and my pseudonym, and the last time I registered a copyright it was $55. I could just register with my pen name (because that's what's on the books and while I don't have reason to need to hide my real name, I'd just as soon keep my real name out of it as much as possible) and only pay $35, but my understanding is that the term of copyright protection is different for copyright registrations that are done only with the pseudonym. So I put both names down.
I also register mine before I publish the paperback. You're required to send in the best existing edition. If the book is only published digitally, you can send a digital file, but if it's published in paper, you have to send paper. I did that once. It gets expensive, buying the books (they want two copies), getting them shipped to you (can't ship them straight to the copyright office because there's a document you have to print out and include) then mailing them to the copyright office. It also took a lot longer to get the certificate. But the actual registration didn't cost any more.