I enthusiastically recommend Cloudways for WordPress hosting. I’ve now moved more than fifty clients there, and I host my own sites there, too.
They add a management layer and optimized configuration on cloud-based VPS hosts. I usually like to use Vultr as the underlying host, as it’s performed very well in my tests, and is also the least expensive option (win-win!).
A 1GB Vultr VPS with Cloudways, properly configured with WP Rocket Cache, and the Cloudproxy Firewall/CDN (both are included in my WordPress Support Services) should be able to handle up to about 500,000 pageviews per month (and maybe even more) — and it’s just $11/month.
They also offer 24/7/365 chat support.
Moving a side involves tons of little details that need to be handled properly, and in the right order. I’ll follow my a 50+ point checklist that I’ve developed over dozens of migrations, to properly configure and optimize your new server and transfer your site seamlessly, with no downtime.
We’ll also set up a free Mailgun account, which helps improve deliverability for “transactional email” (such as password reset emails and new comment notifications). Finally, I’ll guide you through any DNS changes and email account activation as needed.