So, how many users will your site handle without having the web hosting provider suspending your hosting account and sending you a nasty email? Frankly, I'm not sure. But a client of mine got her account suspended when her online advertisement (Facebook CPC ad) brought about 90 users to her site at about the same time. Normally, her site will have about 20 users online most of the time.
Okay, what about choosing a web hosting provider? Well, just choose from the more reputable hosting providers. Zen Cart server requirements are similar to most other programs and hosting companies should have no problem with that.
Having said that, I did still face some issues with a couple of hosting companies:
1. Hosting company A - PHP runs with Safe Mode turned ON
Zen Cart seems to run okay but Image Handler 2 just won't run properly. See this forum post for more info about servers with PHP Safe Mode turned ON.
2. Hosting company B - No cURL support
Zen Cart will run without cURL but some shipping and payment modules require cURL
So, if you're not sure, ask the hosting provider first!