The domain registrars that we've had reasonably good experience with are these:
http://namesecure.com/
http://mydomain.com/
Each offers an array of services that you might find useful.
I don't know who legwon uses but so far it seems stable too.
==========
For free space, there's usually trade offs. They usually want pop ups or banners to appear on the page someplace. The free hosting business is not what it used to be. But these are probably the top three.
http://geocities.yahoo.com/
http://angelfire.lycos.com/
http://50megs.com/
You can also seek out free host indexes such as this one
http://www.thefreesite.com/Free_Web_Space/
However, most ISP's offer a bit of space as part of the connection package. If yours does, then maybe it's best to begin there, and learn the ropes of making web pages before committing to anything serious.
Note. If you are using a free host, then you do not need a domain name.