Usually for the "normal Dude" a shared host will do it because the
webhosting companies usually watch that every client on their server receives pretty much the same RAM and CPU capacity without them to risk to limit it out. At first you should check if my website meets some requirements they are just mandatory for publishing a website like:
image sizes, are you running any memory and cpu intense php or js scripts, are you working with a huge database like e.g online stores with thousands of products would require, are you offering download services or are you even a game hoster. Is your website coded as per web standard?
My recommendation is you to check out and compare several Business Server Hosting Companies and compare them and do some research in Forums on the subject. If you are really unhappy you always can move to another Hoster or upgrade your account to VPS hosting. Ask yourself if the price difference between shared and VPS really is worth it or if maybe you can do something to increase the performance of your website yourself.
I'm running an online store myself with quite a few products and many many product images and I'm using a shared hosting web space and have encountered no problems at all yet.