Migrate Our website to another server

I need assistance in migrating my site to another server. I have not chosen a new server yet, but it will be a dedicated server. Need advice on what would be best to choose.

1. Migrate my site to a different server
2. Assist with an API feed (change IP address)
3. Make sure the site is fully operational (all API feeds working) before we go live.
4. Assist with changing my DNS address in GoDaddy
5. Block all access to the previous developer, both on the site admin and the cPanel. Making sure that they have no access whatsoever.
6. Remove all references to the previous developer on the front end of the site.

NOT part of this project
There will be several other bugs that need to be fixed later on, depending on how well we work together on this project.
The site is a Property resales site. Mainly receiving its listings from an API feed (json). We are using WordPress.
API feeds, both in and out are faulty.
Previously all properties from the incoming feed (json) were stored in a database, both text and images. Now it’s only text stored and images are dynamically downloaded. This must be reversed
A long list of bug fixes.
New functions need to be implemented.