Well, I'm a newbie to the web site world... but here are two that I know a little about:
Dreamhost.com was highly recommended to me last year. I almost went with them when finally signing up for hosting just recently, but decided on godaddy.com instead... because as a newbie I needed the customer service aspect more than anything.
I'd had a domain parked with them for awhile, so called them up to ask questions. They are always professional. 24 hour customer service line. I've never waited more than a couple of minutes for a tech no matter what time of day... and the few times that I needed extra help, they were patient and spent quite a bit of time on the phone with me, until my issue was resolved. There was never a "let me call you back"... they solve the issue while you're on the phone.
The more seasoned programmers on this board may have differing opinions, but that's my 2 cents worth. Check out their sites. Dreamhost is running an anniversary special right now.
~ Debbie