I recommend GoDaddy.com for your web hosting needs. They are priced very reasonable, and so far have provided me with decent service (both web service and customer service).
I used to recommend 1&1 web hosting, but they jerked me around, so now I not only DON'T recommend them anymore, I actively tell people NOT to use them.
I had to move several of my domains and hosting to GoDaddy a while back because of problems with 1&1 and everything was very smooth. I haven't had ANY problems with them so far (knock on wood) and my sites have been up and quick.
I host my videos and downloads on an Amazon S3 server since GoDaddy has limitations on the types of content you can put on their sites. So the site itself runs on GoDaddy, but the videos load from Amazon.
If you're taking my ASP or Frontpage classes, make sure to sign up for MICROSOFT hosting. You will need Frontpage Server Extensions (which they will set up for you). You do NOT want the Linux server with PHP.
(As of right now, Feb 2011, they have a basic Windows hosting package for just $4.99 a month which is perfectly fine for MOST sites).
Any questions, post them here.