One of the questions that I get asked constantly is where should I host my website.  My initial reaction is that you should host through your designer if they offer the service.  Why?  Simply because if your site is on their servers the moment it goes down (and it will at some-point, technology is not perfect) the design service will be trying to get it back up ASAP.  If you are hosting it on your own, you may not know your site is down right away and when you do find out it is down you will need to deal with tech support to get it back up.  Or you can pay your designer to do this for you.

If you do want the money savings of hosting your site on your own.  I think one of the best hosts for the price is 1and1.  They offer cheap small packages which are usually plenty to serve small business needs.  They also offer pretty decent tech support for the occasion that there is a problem with your website.