I don't know how your current hosting is setup, but you should be able to download all of your files off of your website (via ftp).

If so all you have to do is....

1) Download your current website
2) Find new hosting, either transfer your domain, or just point the nameservers to the new hosting.
3) Upload your website to the new host

You won't have to recreate your pages, and you shouldn't lose customers (There could be up to 48 hours for the nameservers to change).

This is all assuming you can download your website from your current host

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