200 yds should be enough, unless you hook a +10lb bone.
For 2-4 pounders 100 yds is usually enough.
A large arbor reel makes retrieving that backing easier. Or you can fill a big standard reel first with dacron and put some gelspun on top so that your rate of retrieval stays adequate even with 150-200 yds out. The weight of the reel is not so important in bonefishing as you're not casting a lot.
I've only used Orvis and Lee Wulff gelspun and found both ok.