The primary difference in most hosting plans has to do with disk space and bandwidth. Those two factors are enough to heavily influence the capabilities of a web site or network of sites. If you want your site to perform ideally then you should consider using a web hosting plan with plenty of both of the aforementioned features.
The effects of disk space limitations differ depending upon the kind of web hosting plan. For example, some hosting accounts will give you access to more disk space if it is needed, like VPS hosting. Shared web hosting, while cheap, also offers unlimited bandwidth. Shared web servers split up serer resources amongst hundreds of sites to give each site the unique advantage of being part of a network of servers.