It depends on what a fair amount of traffic is to you? For a solid shared wordpress host I recommend BlueHost. You mentioned you wanted a recommendation "on the cheap". You can get $50 off through http://www.hostingplanrebates.com. For a virtual private server (VPS) check into liquidweb and lunarpages.
Anybody have a good recommendation for a solid Wordpress host that can take a fair amount of traffic on the cheap. Having problems with my <a href="http://www.psychicchatsonline.net>Psychic Chat Online</a> host. We're currently using the same cluster setup that we use on Trendpimp, and it's just not cutting it for wordpress.