This is an important consideration for anyone developing a website. Domain Names are very useful for many reasons. A catchy domain-name could even be considered a good investment. The main advantage of a domain name you own is that you can move it to any web-host without breaking any of the links that have been made to your website. URL could also be much shorter to remember when directing anyone to your site. It is best to select a domain name with about 6 characters, which is simple to remember and spell unambiguously.
If you plan to host it at an educational site at any time make sure it has the .ORG extension.
Sites like mydomain.com provide lots of free services for domain registration and domain redirection. You can own a domain with a few minutes to enter a simple Form charging the $9.95 for a year to your credit card and know nothing of the details of the registration process, or pay anything for monthly hosting or parking etc. Renewals are currently $9.95 per year and you can do so for many years in advance, but since prices have not been increasing much, this may not be useful. It is still $35 per year via network solutions which was the only choice many years ago. I did some investigations and find that whatever domain registration service you use it is a finally entered into the same ICANN Internet database and once that is done it is independent even of the existence of the registrar. However ensure the domain is registered with you as the owner and administrator, there are some "Cut-rate" registrar's that offer cheaper rates, but require you to pay hosting fees or a retain administrator privileges and charge a fee to move or sell the domain name.
Another advantage of a domain is that you can own your own E-mail address and make sure you never need to change it ever if you change your ISP. You use a service like mydomain to forward your E-mail to what ever mail service you are currently using. It also create as many E-mail addresses that you want for different applications.
Even if you are developing the website as a part of your own website at an educational institution, or hosting it at the number of nominal charge or advertisment driven web hosts on the Internet you can use a free service to point your domain_name to the home page of your website. Note however that if this redirection displays your domain name, or that of the actual host, that is what is bookemarked by reader. If it is the actual host and you decide to change hosts, all links and bookmarks will break. There is ways to do hidden website redirection which displays your domain name but that then hides the rest of the URL as well and page does not get indexed properly in search databases like google. A regular access over a few months found that website redirection was statistically only about 90% reliable, due to server overload or down-time. However if you have a computer permanently connected to the Internet with a static IP on which you have root access to run a server, then you can use free service to point to the IP of this computer. This makes the link independent of needing a redirection from the free server. If you then do nslookup of your domain_name your get the IP address directly from your local name server. You also don't need host organization authorization to point your domain_name to any .org website. However NEVER register .com or even .net and expect to be able to do this at an educational institution. They can and will probably shut you down.
You need to do some research when selecting a ISP to host a domain. The price of hosting has gone down very fast over last few years. The most economical host, giving best sevices for the price keeps changing as new ISP's try to win over a customer base. After an ISP has grown it's customer base they don't need to compete since most don't wish to bother to move servers after they have found one which is reliable.
The cost is based primarily on the disk space the provide for the website, the bandwidth they provide for traffic. In 2004 October, lakdiva.org was moved to a commercial website at Siteground. The reasons for selecting this site were the low entry level cost of $4 per month for 1 GB of space and 20 GB per month of traffic, as well as the Linux server on which they gave me a bash shell account for an extra $24 per year. The server had lynx and when informed they even had g77 installed I didn't look any further. Within just over 1 year by 2005 Dec, the entry level fees had gone up by just 25% to $5 per month, but the allowance had increased to 12 GB of space and 500 GB per month of traffic.
Most personal non-commercial sites don't need this much disk space or bandwidth. Web Hosting is a very competitive. You may now find other hosts for lower cost which satisfies your requirements. However one must carefully consider the services provided, the cost of upgrades, the response of the servers, how long they have been in business etc. I had no motivation to change since the savings I may get will not now justify the time and gamble of such a move.
In 2006 July siteground.com terminated ssh access and I moved to BlueHost.com. They gave 15 GB of Space and 400 GB per month of traffic, and SSH access for $7 per month. They were growing at over 8% per month in 2006 July. They even included 5 ADDon domains, which although setup as hidden subdomains look no different to visitors to the ADDon domains.
BlueHost used the same Cpanel interface. The web stats from the older host was picked up when moved to the proper subdirectory. The old mail folders were transformed to the format used by BlueHost, and in just 2 days the web site was running smoothly on the new webhost. The UNIX shell account was really helpful to simply tar and move the website
Within one year for the same monthly fee they gave 300 GB of Space and 3000 GB per month of traffic and unlimited addon domains. Within two years they gave unlimited disk space, unlimited traffic and unlimited addon domains for the same price.
The meaning of unlimited however became clear in early June 2008, when sundaytime.lk domain I was hosting for free started puting many popular Video's online. For reasons unknown, probably because of the time taken to download the videos or errors in the setup, this generated a very large number of simultaneous processors on the server. When the usage first became high my account was moved to a faster server. The next week when they detected my account using over 75% of the simultaneous connections on the account when the expected me to use under 2% of the resources of the shared server, the account was suspended till I stopped hosting video's on sundaytimes.lk. That domain is now on a dedicated server limited 320GB diskspace and 3000 GB per month traffic costing aboout 20 times the cost of unlimited shared hosting. Soon after I needed to renew my hosting, and decided to remain at bluehost.com since it was clear that they protedcted the interests of the shared accounts hosted on the same server.
Useful References: Considerations you should be aware of when registering your domain.