You can easily move the website by compressing it to a zip file or something similar. Download the zip file, extract it on the new server. As for the database, first of all, 70MB seems a bit low for that amount of posts. I'm guessing it's more 70GB, depending on the attachments. But if you use cPanel, you can easily download the database and import it on the new server. Then you point the domain to the new server/nameservers and wait for DNS to change over. That's it.
It's peanuts really, I've done it countless times. So if you need help, feel free to ask.