I don't really have any reccomendations, just that you shouldn't be paying any more than $20 a month for web hosting. If I remember right i think it costs about $15 a year to register a domain name, though when you register the domain and have the web-hosting with the same company, you can sometimes get a discount. =-)
Also, what program are you going to use to design your webpage? If you've got a computer with Microsoft Frontpage installed... I've never used that program so i don't know how good it is, but it seems pretty much all the hosting companies are compatible with it. if you're using something different, though, you might wanna consider going with what the program reccomends. When I first tried to start my site, i had compatibility problems between the program I used and my hosting company, so i had to switch.
As far as website designing programs go, I choose the first one I found under $20 and that was a HUGE mistake. =-) Unfortuately most of the good ones are like $200 and up, but I've head there are some decent ones for around $50 and such.
Ha ha, but anyway, i'm by no means an expert. As far as computers go, I know my way around the word processer and that's about it. =-) Good luck!