The best stones for you are Shapton GS series. They're a little expensive though, and might be something to aspire to, more than something to purchase -- for the time being. Norton makes very good waterstones. It might not be a bad idea to purchase a set, and as they wear out to replace them with others. Sharpening Supplies sells a two combi-stone, four surface set (220, 1000, 4000, 8000 ) for around $120 -- including a flattener. You'll also need a "prep" stone for the higher grits.
Water Stone Kit
If you can sharpen a knife with any confidence at all on the tri-stone, you can reprofile the UX-10 and sharpen it to a fine edge indeed on any adequate waterstones.
Also, depending on the condition of the stones in the tri-stone and their grits -- you can probably reprofile the UX-10 on it just as well. A polished edge is another story. Norton's finest man made stone, the fine India, is actually pretty coarse; and their finer and polishing stones are Arkansas -- which is marginal on steel as hard as a UX-10. It will do the job, but it's very slow.
The best waterstone grit for profiling a UX-10 is around 200#, such as a Norton, King or Shapton 220#, but you can go coarser or finer (good idea if you don't trust yourself). I wouldn't want to use anything finer than a 500# Shapton GS, which is very fast considering how fine it is.
The coarsest stone, on your tri-stone, probably a coarse or medium Crystolon or a coarse India will do the profiling as well as a waterstone, providing it's not clogged or glazed.
Two other good choices are the DMT XXCoarse and XCoarse diamond stones. If you go DMT, remember to use very gentle pressure all the way through. These stones cut very fast.
Here's the technique for reprofiling: Start by marking the entire edge bevels, on both sides from front to back with magic marker -- in fact, to black (or red or blue) the first 1/2" of the blade. Then lay the knife on your coarsest stone (at approximately a 15deg angle), and feel for the manufacturer's bevel, by moving the knife in little circles, or Ws with very little pressure. When you can feel the bevel, hold the knife at that angle, and slowly and gently try to grind the magic marker off the edge. Do this on both sides until both bevel edges are cleaned.
Now compare the bevels. One is much longer than the other. If you hold the knife by the handle, the side to the right of your hand will be longer, and to your left will be (duh) shorter.
The bevel angles are the same -- in the case of the Misono, that's around a 15deg edge angle.
Start grinding the short side on the stone using circles or Ws -- and moderate pressure. Every few passes check to make sure that one area of the knife isn't moving much faster than another. Also, compare the bevels as you lengthen the short side. Don't hurry, you'll be at this for awhile.
As you work, inevitably you'll find that some parts of the knife grind slower than others. Correct that by "sectioning" the knife. That means grinding back and forth using straight up-and-down strokes so you only sharpen one section at a time. When you've got it even, go back to using your grind strokes that move the knife across the stone as well as up and down it.
Eventually you'll have the bevel you're working on will match the factory bevel. The knife is profiled 50/50. All there is to it.
The UX-10 is not a difficult knife to sharpen at all. Sharpen it in the regular way. I'd suggest polishing it to between 4000# and 6000# with Shapton, or 8000# with Norton, If you want a "bright mirror" polish, you're better off using compound on lapping film or a strop, than a stone. Stones get ridiculously expensive and don't do a much better job.
Although it's on the expensive side, I'd suggest looking at one of the EdgePro Apex kits. If you're obsessive enough to set it up every time you want to sharpen a few knives -- it's a good system with a relatively shallow learning curve.
Your idea to practice on an el-cheapo or an old beater is, of course, a good one. Some practice in holding the angle is very helpful. More than anything it's developing the confidence. Freehand sharpening isn't difficult. Not even doing it well.
BDL