Migrating an existing website to another host and check website performance -- 2

I am now interested in moving an existing website (Wordpress-based) from Bluehost to another host for a lower cost and similar performance. I started managing this website about 3 years ago on Bluehost, it charged an introductary low price, but now it will charge the regular price, which is more than 3x expensive. Here are what I think. (I will disclose the actual domain after being contacted. It is a simple artist website with 9 sub-pages, with calendar and contact form, etc.). 1. Migrate the entire website from Bluehost to somewhere else, probably Dreamhost. (Or A2 or Hostgator, if you recommend) - I think you can use the automatic migration feature. (Dreamhost says it provides Free Automated WordPress Migrations.) But please check if things are all good after the migration. - Need to use info@domain at the new host. It is good to backup the previous emails, but it is not necessary. - Advise how to make sure the site is backed up every day. 2. Transfer the domain from Bluehost to the new hosting company. 3. Check website health. Is it secure, updated, fast enough at the new host? 4. Is there a way to get some statistics, for example, how many visits to each page? (The numbers should be visible only to me.) 5. Set up Cloudflare (or something like it) if provided for free