Your question is deceptively vague because Ubuntu server would operate similarly to any other Linux distro, so the answer you're looking for might be more dependant on your specific needs. For that reason I'm going to post quite a verbose answer in the hope that some of my points answers some of your questions
Ubuntu Server, as a server OS, will support all the same hardware that Debian, CentOS and all of the other Linux server OSs would support. They're all just Linux at their core. And despite with some might lead you to believe, Linux's support for server hardware is generally really good (in fact better than Windows, in my personal opinion, as you don't need 3rd party driver CDs etc).
With regards to running a website, the software isn't Ubuntu specific. The most common set up is often referred to as "LAMP", which is L
ySQL and P
HP. This set up will work on any Linux distro as Apache (the web server, referred to as a "HTTP daemon"), MySQL (the database) and PHP (the server side web programming language) are all platform agnostic. In fact you could run Apache, MySQL and PHP on OS X and Windows (known as "WAMP") if you wanted to.
You can, of course, run other HTTP daemons (lighttpd and nginx are other popular ones I've used). Just as there are other databases eg (PostgreSQL) and server side languages. And you'll find that some server side languages require a slightly different framework (eg JSP (Java) can run atop tomcat; Go, Python and Ruby can run as their own HTTP daemon). But it's probably best to stick with the typical LAMP set up if you're new to this.
The difference Ubuntu Server makes to other Linux distros is purely a systems administration thing. Personally I don't like Ubuntu Server as it installs a lot of unnecessary stuff and prefer to run my servers with as little installed as possible. But Ubuntu Server is stable and used in data centres, so I should stress that my dislike of Ubuntu Server is purely preferential.
Ubuntu Server will install without a GUI - so you'll have to be prepared to get your hands dirty in the Linux command line. If that might be an issue then I'd suggest installing OpenSuse instead and using it's administration tools ("yast") to manage the server. However, if you want my advice, you are better off getting familiar with the command line because it is more powerful that GUI tools (which is why us sysadmins still favour it)
Anyway, I'm sure I've covered some stuff you're already aware of, but I hope I've also answered some questions