Web page hosting?

Ummmm, Help?

I have no idea what Im looking for...

My dad has a crappy one page web site for our auto appraisal service www.autoideas.net and I would like to transfer it to a new host and redo the whole thing with at least 2 email accounts and set it up so that there is more than one very crappy page along with being able to do online appraisals. He knows nothing about how to work it and said that I can redo the whole thing. My brother in law knows HTML and said that we can build the whole site in one day with the outline that we came up with.
What will I have to do to transfer autoideas.net to a new host, is it pretty simple to do?

This is what I came up with options for a host search.
http://www.findmyhosting.com/searchresults.asp?page=1&op=1&sid=1636666