i would think for tarpon you'd want the largest arbor possible relative to the rod. you'll appreciate it when you're reeling it in. that said, you'll want 250 yards of backing-maybe more depending on whether or not you're on a boat.
as for the battenkill reel, i'm not sure that that's the way to go. i think you'll need a heavy duty salt water reeland if my memory serves me right the battenkill is a fresh water reel. anyway, there are plenty of moderately priced reels around that are made for salt water conditions. i'd check out nautilus or danielson..