Yes to the cooler . Any good brand PSU with 500 or more watts should do fine , I like a bit of overhead , I use the Antec HCG 620M on my fx 8358 7850 computer . Picked it up on sale for 65.00 . Look around for sales on Corsair , Antec , XFC ans Seasonic .
And the last place to "cheap out " is the PSU . You want good stable clean power , especially if you're going to OC