Is it better to travel business class on the ferry's as opposed to economy? I am wanting to travel between Santorini and Paros, Paros and Athens...

They allow smoking in economy and don't in business....or at least it appears that way. The smoke was so bad on our ferry that we asked to be moved and payed extra to get out of it. It was worth the extra!

No reason to go anything other than economy. On a daytime summer ferry you'll probably spend much of the time outside on deck anyway. You can still go inside & use the cafes & bars.
The only time to consider anything other than economy is an overnight ferry when you may want a cabin. I can't think of any reason to buy business class at all!

Your info is out of date southeastern. Laws that came into force on 1st July 2009 forbid smoking in any of the inside areas of a ferry, so that is no longer relevant. You can smoke outside on deck whatever ticket you have paid for.

Is Blue Star the name I'm looking for?

Yes, that is the main ferry on these routes.

thank you very much!

http://www.bluestarferries.com