For spinning reels I am planning on braid with floro leader and mono backing. My main question is what is better for backing on a casting reel, braid or mono backing to floro or co-poly main line?  Any thoughts would be greatly appreciated. 

Since backup will most likely never be used, doesn't much matter what it is.  It is there to simply take up space. 

Cheap mono

I use cheap Berkeley Vanish as backing for both spinning and casting.

10 yards of mono or copoly backing to nearly a full spool of braid, to a mono, floro, or copoly topshot or leader. Mono and copoly are much easier to tie to the spool than braid because of stretch. I use straight copoly for all lures over 1/2 oz because even heavy braid will occasionally break on a mild backlash with a lure over 1/2 oz. Strange but true.

I use whatever I have left on a spool if it's almost gone but usually I try to make it mono for both casting and spinning.  

Big diameter line, either braid or mono is best for backing, to keep the loaded spool mass down.  When I'm topping deep B/C spools with braid, I use 20-25 yds 20-25-lb mono for backing.  Big diameter line doesn't pack efficiently on the spool, and forms a lighter-weight spool arbor.  Both large diameter braid and large diameter mono are less dense and, therefore, lighter weight than fluorocarbon.  

As has been stated, what type of line you use for backing has zero effect on the mainline. The reason folks started using backing with braid was the cost of braid vs. mono and the fact that braid would slip on the spool without something to grab on to. How much backing you use is up to you, but remember that 40yrds. of mainline is all that you'll need, unless you have a strong wind at your back. More than that is just a waste of braid.

Thank you for all the info!  I appreciate it.