Server migration?

My Comcast cable connection is terrible. While the machine that hosts my websites is fine, the lack of a stable connection with Comcast requires that I move my website to another server.
I’ve never done this before. I’m scared. I’m currently running SuSE Linux. Frankly, I never touch it unless I have to — just let it quietly hum away.
So, how do I migrate my WP sites to another server? My main site is 2 WP installs and a phpBB working together.
Any pointers would be appreciated, along with recommendations for some inexpensive and reliable US hosts.
Thanks!