I think that is very good budget for the shared web hosting account. Find some related offers here in the advertising forums and then try to find out more reviews. I think that is the best method to find great host.
Hostgator is the best by far. Coupon Code: ULTIMATECOUPON1 will give you $0.01 hosting for the first month. I host 4 phpbb forums for $7.95/month on Hostgator and over 20 add-on domains. Never had a problem and their customer service is awesome.
Why not try a reseller account? That way you can not only get back what you pay to host your own sites but make a profit since you can host unlimited domains with most reseller hosting accounts.
I f you think Godaddy knows anything about hosting, good luck. They are good only in being a domain registrar and that is all.
Like many other people i would go for hostgator they are simply the best host. :') Link to them in my signature.
You should be able to find a decent Shared, Multi Domain Hosting service. My advise is to sent requests to a few hosting providers to be able to compare their responses.
I use Knownhost.com as my host for a high-powered VPS system. They offer top-notch support as well and will install code and error-check code for you as well.