We are looking to start a Drupal driven website and need someone to get the final site looking & functioning as we like it. Would we need to hire a web designer or web developer? Or perhaps an agency who does both?

Probably both, the definition of what a designer or developer does seems to vary quite a bit, and it sounds like you need both technical and "look and feel" type work.

http://tokatlilar.org
http://www.haytekltd.com.tr

i design its but i live in turkey :)

You should look for a team that has got expertise in Drupal, since you will need a coder, a designer and both should be familiar with Drupal.

Agency is good if you have money.
If you want to lower costs and know what you want then hire a Drupal developer for the backend stuff. Use web designer to develop the front end.