The majority of websites are hosted on a shared web hosting server. Shared hosting has a lower cost than any other hosting type so it's a huge draw for many sites. Small websites or personal sites and blogs can run fine on shared hosting accounts, but hosting your Rails website on a shared hosting server is not a good idea.
When you buy a shared hosting account, you are given space on a large server run by the hosting company. This server can have several thousand sites of various sizes crammed onto it. Since the server has a limited amount of power, all of these sites have to fight for their CPU, bandwidth, and memory resources. All it takes is one website to hog all of the resources before everything slows down.
If you want to host a Ruby on Rails site, there are much better options than shared hosting. Both dedicated servers and virtual private servers will give you exclusive access to the resources that Rails needs.
A dedicated server basically means you get an entire physical server to host your Rails sites on. In addition, a dedicated server will give you root or administrator access to the server so you have the authority and control to change anything and everything you want to. For Rails this is a great option because you can tune the server specifically for your site and don't have to settle for the generic Rails hosting options most shared hosts provide.
However, you will need some technical expertise to manage a dedicated server. Typically most of the management comes in two chunks: set up of the server and ongoing maintenance. The set up portion will take a lot of time, especially if you haven't hosted Rails before. The best advise is to read up on the different configurations available and try them out several weeks before your want to use the server for your live site.
Ongoing maintenance for a Rails site is pretty easy if you plan it out ahead of time. Make sure to setup monitors for your resources (disk space, memory), add alerts if the resources are being consumed too fast, check your backups, and set aside time to do software updates every month or so.
However don't think you need to manage a dedicated server alone. Most hosting companies have a support team who can give you a hand or answer most questions you have. You can also order a fully managed server. A managed server is a dedicated server but the hosting company maintains the server for you. This extra service doesn't come cheap, you can expect to pay two to three times the cost of a dedicated server if you want the web host to manage it for you.
Whenever you are looking into dedicated servers, you need to ask yourself if you need this extra power. If your Rails site has gotten a lot of traffic or you are planning on fast growth, then a dedicated server might be the best thing to host it. Remember, you can always start with a small virtual private server and upgrade to a dedicated server later.
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Before you go; if you are looking for Rails hosting I've been writing about it to my blog.