I'd agree on building a cruiser-heavy force.
If both of you are mixing and matching, I'd suggest an ideal end-state of two-to-three of each cruiser class, and one to two of each heavy cruiser class. You can mix them up in whatever way you like.
phydaux is correct, the two classic chaos lists are a big carrier group or a line-astern broadside force, but that's not the only options.
A line abreast lance force can do surprisingly well if you go in for it in a big way (two Murder-class and a Hades-class heavy cruiser put out eight 60cm range lances - enough when Locked On to cripple an imperial cruiser straight through their shields and frontal armour from outside the ship's own range)
Slaughter-class are good but best used as either Daemonships with the Mark of Slaanesh (because no command checks ever for your enemy) or World Eater crews, because they have the speed to board and the close range firepower to achieve something if they fail to make contact. Both are great tools versus necrons (since the tinbots are critically dependent on passing leadership checks and boarding damage ignores brace for impact), but less important against other chaos ships - although since chaos has comparatively low armour, a fast, close-range flanker can't hurt.
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