Moving to a new host

This may be slightly OT and maybe a bit of a newbie question. I'm finally moving to a Rails-enabled host, and I'm starting to prepare for what is needed. I signed up with HostingRails since they really seem quite keen on RoR and their charges are quite decent for a starter.

The main thing I need to do now is to point my domain to the new host. My domain was a free domain provided by my hosting provider but I have full control over the name servers, etc. I do, however, need to renew the domain now.
1. Should I transfer the domain to someone like GoDaddy and then renew it? Their cost for the 1st year is quite nice.
2. After that, I need to change the name servers. I guess I log into GoDaddy (or whoever) and make the change? Does anyone have any idea what the settings for HostingRails are? I couldn't find it on the site? (Perhaps, it will be there in the email they send me, I'm not sure)
2. Is there a period of time when services will be unavailable to me?
3. I guess I shall need to create all the email accounts on my new host after that?

I'm sorry some of this is very trivial, but this is the first time I'm needing to do a transfer!