What size line?

If your putting on enough braid that you'll never see your backing, 15(or even 4) lb is fine. If you plan on seeing your backing I would go with 5lb heavier than the mainline.you don't need allot of backing to get the braid to grip the spool just a few yards. But if your trying to use as little braid as possible to cut costs I would go with heavier backing.on a side note I was flathead fishing on the river one night and fell asleep. Woke up in a daze in the early hours of dawn. Started reeling in one rod that had 30lb braid and 4lb backing only to find that a fish had taken my bait, all 300 yd of braid and nearly all my backing(though I didn't realize it at the time. Black line on a black spool is hard to see in the dark.) A soon as I came tight I lost everything save for about 20ft of 4lb backing. Felt really bad to leave all that line attached to a fish. I run heavy backing on my cat rods now.

I'm getting ready to reline with braid too.  I was thinking similar for backing.  I'd hate to have something really nice on with too thin backing.  Too thick and the knot is an issue.  Also wondering if that mono will deteriorate?
 
FishinGuy, what do you use as backing on the cat rods?  Mono or some sort of Dacron ect?

I now back my cat rods with the same heavy mono I use for leaders 40 50 or 60lb ande mono. But I don't use very much, just a few wraps to nearly cover the spool. And an improved Albright for the connection(double over the mono, not the braid.) I would think that since the backing is completely covered with the braid it won't get any UV and shouldn't deteriorate as fast, but if I replace the braid I replace the backing. I've never had my braid slip on the spool, but have seen it happen to others multiple times. BH your 15lb should be fine.

I use 30# Ande or Trilene Big Game...cheap and tough.