Is it good to use a content management system or build a classical website?

Please let me know the advantages / disadvantages of each

I'm a web designer and web applications developer, fully capable of building a framework and a full CMS from scratch if need be (and would actually consider it a fun project, if I could find someone with the budget to pay for it).

That said, definitely go with an open-source CMS. For ease of use, the order would be WordPress, Joomla, Drupal -- though with the latest version of Drupal, it's gotten significantly easier to use.

For power and flexibility, search engine friendliness, and selection of add-in modules and themes, again in my order of preference, Drupal, then WordPress, then Joomla.

Almost all of my sites are Drupal-based. One of the huge selling points is that you almost never find yourself in a situation where you have to have multiple systems talk to each other... for example, when you want to run an online store with your Drupal site, there's no need to install a shopping cart application like osCommerce or ZenCart. Instead, just install Drupal's excellent eCommerce add-in module.

Here are a few Drupal-based sites that I've launched...

http://HesitantRhino.com
http://Questions4Change.com
http://TorranceChurch.org

Also in the running... for an online classroom environment and training type situations, consider Moodle. I'm in the process of building a course on site development using WordPress right now. Drupal is next. Log in as a guest if you'd like a peek...

http://training.HesitantRhino.com

For more academic-style work, with multiple professionals or other people knowledgeable in their field collaborating in online documentation and research, consider a wiki. Some wikis can be memory hogs because they include everything but the kitchen sink. My favorite, for both features and light weight design, is WikkaWiki

But back to the design question... once you've selected the CMS of your choice, all you need to do is edit an existing theme or build one of your own to give the site a unique look-and-feel, and perhaps program an additional add-in module or two if you have a need for some specific functionality unique to your site's operation.

The other option would be to go with a framework, like CodeIgniter or CakePHP, which is still a lot better than re-inventing the wheel, at least when it comes to the programming side of things...

http://codeigniter.com/
http://www.cakephp.org/

CMS! All the way!

If you want a blog, WordPress is the way to go.
http://wordpress.org

Builing a classical website is harder because of the coding, updating, no WYSIWYG editor (although I don't like those). There is also Joomla, Mambo, and e107 (CMS's).

I love WordPress - and I use it all the time. It's just that I like my blogs, and sometimes I need to create pages.

if you have time and exact view of what is required it is always better to reinvent the wheel.
1) you will learn a lot
2) you will have a complete control on programme.

if you don't have time and just want to set an CMS

you can try

joomla
or
drupal

they are highly customizable and there is always a learning curve for everything which does complex things! :)