This is usually the cheapest option and in many cases just what you need when you’re starting out. Linux web hosting plans come as little as a few dollars every month. You need to study your potential web host though, read some reviews etc. You’ll be sharing a web server with possibly hundreds of other websites and if the web host is only about making money by stuffing as many websites into as few servers as possible, you’re going to experience poor performance.
When your site outgrows the shared Linux server, ie. many visitors, you’ll have to upgrade to a different server and move all your stuff over. Some web hosts offers an easier way of doing this rather than having you move your files, database etc. manually, so be sure to check that first if you expect your site to grow into having thousands of visitors per day.
Basically the same as Linux hosting above, but might be slightly more expensive as some web hosts, due to Windows licenses and such, I imagine. The same warning applies here, as you’re still sharing a server with many other customers.
Reseller hosting is what the web hosts calls the packages that are slightly more advanced than the standard Linux and Windows hosting plans. With reseller hosting, you’re basically also able to “resell” hosting space, ie. you can host websites for your own clients on the server as well.
VPS stands for Virtual Private Server and is almost the same as having one full dedicated server to you, yourself, except that you’re still sharing the actual physical server with multiple users, but each of you have a dedicated amount of ressources such as CPU cycles and memory assigned. This means, no matter how many visitors other websites on the web server are having, they’re never going to use any of your ressources (CPU and memory) and the performance of your web site is not going to be affected.
VPS hosting are more expensive but also offers greater performance and often you can upgrade, and downgrade, as you need. So when your site grows, you can just purchase more CPU cycles and memory – and you’re all set.
Finally, the dedicated server plans. Here you’re buying (renting) a physical server which is yours to use and nobody else. You’ll often get Remote Desktop access as well, so you can use it just like any other computer, more or less. This plan is also expensive but if your whole business depends on server uptime, you might want to spend the few thousand dollars a year it costs to rent a dedicated server and get the best performance possible. Keep in mind though, in case you’re not tech savvy enough to maintain it yourself, you’ll need to find a web host that offers managed dedicated servers, either included in the price or so you can pay them to do whatever stuff you cannot figure out yourself.
Dedicated servers usually also comes with a control panel, like the other hosting plans, so most of the web related stuff is just as easy to do as all the other web hosting plans.
There’s much more to web hosting than explained above, but at least now you have a little knowledge about what’s what and you can continue your search from here.