Migrate from asp.net environment to normal shared hosting

I have two websites: https://supportstofamilies.org and https://mofamilytofamily.org

These were developed on a space at discountasp.net because we were originally going to have custom CMS built for us but that didn’t happen.

I’ve pretty much determined I’m going to reinstall my themes in our new hosting environment (typical shared hosting/Linux cpanel)… is there anyway to copy the databases and back up wordpress and import it somehow or should I just copy+paste and reupload everything??