A safe hosting move is a staged handover
You can move a website to a new hosting provider without changing its domain name or public URLs. The safe sequence is to build a working copy on the new server, test it privately, prepare email and DNS, switch traffic, then keep both hosting accounts running until the new setup is proven.
Do not start by cancelling the old account or changing nameservers. That removes your easiest rollback path before you know whether the files, database, forms, email and SSL certificate work at the destination.
If you are still choosing the destination, compare the new plan's storage, runtime, mailbox and support limits on the Allanux web hosting page before moving any data. A migration cannot fix a plan that is too small or incompatible with the site.