I want a blog as a part of my website and not a link to another website like example.blogspot.com?

Wordpress will work for this. I host a Wordpress blog on a domain. like http://wwww.whatever.com/blog using Wordpress without any problems.

Well, how familiar are you with websites and webservers? Do you know any html/css/php/sql? I think there are a great deal of questions to be asked before I can recommend anything – although I will anyways.

I would recommend a hosted solution. Wordpress has partners that host wordpress sites that’ll make it really easy for you to get your site up and running. You may want to check there first. If you’re comfortable hosting your own site, find a webhost you like and buy hosting and a domain name. If you need more help, just come back with more questions! =)

Try using Simplescripts for a no-fuss install on your own web server, under the directory you dictate (I recommend ’/blog’ i.e yoursite.com/blog).