Hello Kian!
It is nice to meet you here and welcome to the forums!
Actually most of web hosting will support your web application (wordpress).
Other problem you could expect - size. In this case you need to understand that on shared hosting account that would be really hard to get ahead.
I recommend you start your voyage from VPS.
Check
http://chicagovps.net/
There you will be able to find VPS below $7 and friendly and polite support.