Transfering servers/host

OK so it looks like im going to have to change my hosting and move my wordpress site.

Is this difficult? I dont have any experience with this, ive seen there are plugins to duplicate wordpress sites but i worry about the databases and things does that take care of all that too? also my new host may be a different web address’s etc do i have to change all that in the files too? It all seems a bit overwhelming any help much appreciated….. Also would this be something a new host would be likely to do for me?