Site Needs
The type of hosting service you will need depends completely on your applications needs. Many of the types of web sites most people build are generally very simple. They have simple layouts, simple sidebars, simple headers, and the content is fairly static. Most of these sites are built using blogging software such as wordpress. It's the standard for pretty much all the personal websites on the internet right now. I forget what percentage of the internet runs on wordpress, but it's not low.
Most small businesses will go with this type of site. Of course, a small business is not normally considered an internet company, and it does not usually have the need for a large complex site with lots of functionality. For ecommerce needs, wordpress even has plugins that allow you to run a complete product catalog directly within the plugin.
Bandwidth
Pretty much any small website will not need much bandwidth at all. Video and high definition photos do consume lots of bandwidth, but if these aren't hosted on your server they don't use that servers capacity.
Services
When choosing a web host, you will have a multitude of options available to you. One service is not necessarily better than the next, and sometimes the best deal is the best one to go with. Many will offer an introductory cheap monthly rate of three or four dollars and then raise it to six or seven after your initial term is up. All of them are basically going to offer a slightly different version of the same thing with their hosting packages. This can include: mysql, php, pearl, one-click installs for popular software such as wordpress or templates, site builders, drag and drop site builders, unlimited bandwidth, unlimited disk space, unlimited domain names, unlimited email accounts, etc.
All this is very well and good, but everyone company will offer these. You can pay a lot more for a higher priced plan, but it likely won't include any more features that a cheaper company's plan would offer.
The one main feature you really need with any account is cPanel and access to the root site folders. If you ever plan on developing any custom built applications, you will have to upload the software directly the site root. This includes codeigniter applications, drupal projects, and more.
Here is a list of the best web hosting companies out there right now. It's often hard to even know about all of them because there are so many, but most of them are listed on this page.