Migrate a Wordpress site

I have a live Wordpress site hosted on Bluehost. I need to migrate the site to Interserver. The Interserver account is all set up and Wordpress is installed. I have tried to migrate the site via a backup/restore using Updraft, but there seems to be some compatibility problems between the two platforms, possible caused by a different UTF character set on the database. I have set up the Interserver site under a temp domain name as I want to get the site mostly functional before I update the DNS on the main domain that currently points to Bluehost. Looking for someone who know what they are doing to step in and takeover. I know it's a simple job if you know what you're doing, and I don't have the time at the moment to work it all out as I go.