Moving to a new server

hi everyone,
i have a WP install on my server space.

I am moving to a new cheaper hosting plan with my service provider. It will have the same domain.
What i have to do is buy the new plan, then do a database backup, download the wordpress files, upload the files via FTP to the new directory then import the database backup.

is that all i need to do with the files? just FTP the files over.

So i don’t have to do a fresh install of WP on the new server first?
thanking you