I would suck air thru the filter ,then thru the hood , and then thru the fan and out.
If you try to blow air thru a hood , you would have to seal the hood completely in order to keep from blowing hot air out around the glass ect..(unless its a cooltube) Where as sucking it thru the hood ,if you have a little air leak know big deal.
I would definately suggest getting the biggest fan you can afford(within reason)And I would suggest a CanFan
Using a carbonfilter, ducting and cooling a hood will cause a bit of static preasure,and i have found that the squirrelcage fans just dont cut the mustard when it comes to preasure.
I use a 8" Canfan HO 756cfm .I divided the duct into 2 6" ducts .1 duct cools 2 1000s and the other cools 3 400s.
Hope this helps