I just sold my website for $125 on digitalpoint. I need to transfer my domain to this buyer, as well as my Wordpress Blog.

I think I need to get an EEP code or something from my domain register? and send that to the buyer? Then they can do the transfer.

As for the website, do I just download my Wordpress files, zip it, and send it? what about the database info?

Yes, to transfer the domain you will require the EPP Key which you will have to provided it to your buyer and regarding the backup you will have to download all your contents and placed outside the root folder and create one FTP account and provide the details to your buyer so that they can download it at his end.