There are few things you need go get your own WordPress site set-up.
First of all you need a Domain name registered. You can do that at www.namecheap.com
Next is a place where your site will be hosted. My favorite hosting company is Greengeeks.com
They have fast secure servers and they are very affordable.
The last thing you want is a good theme that will help you show your best content and is well coded.
For me, that means that most of my sites and my customer sites are built on StudioPress.com Genesis Framework plus a good responsive StudioPress Child Theme.