Pretty much anything in diamond (DMT, Eze-Lap are among the best) or silicon carbide will be the most versatile, expecially if you plan to reprofile/rebevel any of your knives. Sandpaper (wet/dry type; silicon carbide, from 3M/Norton) delivers the most bang-for-the-buck by far. It's available in a far more comprehensive grit range than anything else, meaning it's MUCH easier to fine-tune your edges to your preference. Being flexible/pliable, you can also wrap it around any convenient shape, like a cylinder (PVC pipe, dowel, broom handle, wine bottle, etc.). That'll come in very handy for the recurve on your ZT-0350. Fold a piece around the shank of a small screwdriver, for sharpening serrations. And the sandpaper can be wetted & applied to a glass backing, for V-bevels, or laid atop a softer backing (leather or mousepad) for edge-trailing sharpening of convex edges. Very, very versatile stuff, and inexpensive too.
The DMT Dia-Folds are extremely versatile as a pocket & travel sharpener. The blue/red (coarse/fine) combo is probably the most useful. The Fallkniven DC3/DC4, as mentioned, can be quite good. Some have had some gripes about the finish/quality of the ceramic side, but I've been impressed with my DC4.
A Sharpmaker is handy for regular maintenance, so long as you don't let your edges get too dull in the first place. Not very aggressive for heavy reprofiling jobs on tougher steels (like S30V), though.