I'm looking for a web hosting solution for my site. It doesn't sell anything,
it's just a web presence for a bricks and mortar business. We've already
purchased the domain name and the entire site has been designed.

Where do I start with a web host? What should I look for?

Thx, Luli.

Look around in this forum and you will find lots of quality hosting companies which can host your site. Some cost more than others, some provide more features etc... but the most important thing you want to get is good customer support.
http://hostmatters.com and http://webauthorities.com are two examples of good hosting companies.

Not that this helps much, but here (http://www.webhostingtalk.com/showthread.php?threadid=3053) you'll find a four pager of some of the hosts that hang out here. Read some threads and see if someone has asked for something that matches your needs. Do you have any special needs?

How much space, will it just be a small site with little traffic for the most part? Or big-n-busy?

Welcome aboard Luli.

I suggest you have a good look at the following two resources :

http://www.hosthelp.com
http://www.forumhosts.com/hosts.htm

These two will get you started on what to look for in hosting. Then start investigating!

Good luck.