I find the best thing to as Byzantium, is to do what Alexis did historically.
Small Grab. Hold, small grab, hold. let the crusades through your lands and follow in behind em, Grab, hold.

The Byzantines postion aint pretty.
In my campiang i had stacks comming in from hungary, the turks and veince all at once.

So be warned.

Make certain you build up your economy. If you do it right, soon enough you will have 'restored the byzantine postion of wealth'.

Cavalry and navy are key for any byzantine strategty.
When you start getting your medium level units, Infantry, lancers, and dismounted lancers, then you can start going to kick some ass.