OK, not sure how this will affects my sites, but I have finally been moved to a Dreamhost Private Server.
I am starting at the lowest level, hoping this is all my sites need. But if I need more resources I can easily add from the Dreamhost web panel.
Was a few hiccoughs during the setup as DH network was slow running, but they were sorting the move. All sorted now.
Any problems noticed, please use my contact form.