You need to know about their uptime owner. Uptime and availability are important.
In case you had just started a used marketing campaign or been handing out much more business cards recently and these new potential clients enter in your web-site address in to their browser and your web hosting provider has overcrowded their systems or has gone down, what will happen?
Well simply, it will time out, they won’t be able to visit your site and would most likely visit your competitor’s site, which has stayed up trouble free all this time! Is it worth risking your business to a less than competent hosting provider? I didn’t think so,
Bandwidth is important. This is major. Without bandwidth your visitors won’t be able to visit you, or even in the event that they do, their visit will be slow, which could translate in to an image in their mind of your business matching. Most providers will let you go the limit, but bill you additional in accordance with how much you exceeded the standard allowance in your hosting plan. This is fine. You can always upgrade later as you build your site and online presence.
Storage is the next major point. You need to know you’ll be able to fit everything for your site in to the apportioned space. In case you run out of space, you won’t be able to fit any more web pages or images in. This is a Bad Thing™
These features are way important and could be all that separates your online store from looking amateurish to professional. For payment processes, try to pick someone local (the money conversion would eat up a component of your profit) or someone with moderately low fees, but probably not the lowest. I do know that PayPal integrates in to osCommerce (free shopping cart and ecommerce software) well and they make a decent combination.