Happy to hear you are interested in our services. I would check with your current web host to see if they offer a way to easily export the mailing list setting and archives, then we will check and see how easy that might be to import back in. With e-mail accounts, the easiest thing to do would be to setup a desktop e-mail application and have it download all of your e-mail from the server. Then, once your new e-mail account was setup and active, you could send to yourself all the mail you wish to store in the webmail account.
We can work with phpBB or SMF, the decision is yours. You might want to check out their profile pages here:
http://wiki.lunarpages.com/Category:Third_Party_ScriptsHope that helps some!