I recommend hostgator for web hosting. The shared hosting baby plan will do... nothing fancy. Don't get your domain there though... get it from either godaddy or namecheap. You want your hosting separate from your domain...
You can use a coupon code to get a good discount on your hosting. Check out
Best HostGator Coupon Codes for the latest discount coupon. I think the best one right now is
HGBEST2011
It gives you 25% off any hostgator web hosting plan =)