I didn't realize synthetic rope was made from so many different types of material
It's really not made of that many different types of material. Spectra and Dyneema pretty much dominate the market. There are many other line types (nylon, polyester, vectran, and single braid vs. double braid), but the only ones really used in winching are spectra and dyneema single braids.
As a life-long sailor, and owning some racing sailboats, I've probably bought 100 times (or 1000 times?) more of this stuff than anyone who's ever putting it on a winch. I have quite literally "boat loads" of the stuff.
It's amazing, it's strong, but it has two weaknesses:
1. UV exposure, so keep your winch covered, as Hay Dude already mentioned.
2. Abrasion resistance.
The stuff I was looking at had a core of Spectra, for strength, and an outer sheath of Dyneema for wear/abrasion resistance.
A dyneema sheeth over spectra would be both uncommon and expensive, at least for sailing applications. We usually see polyester sheathing over either dyneema or spectra, standard "double braid" control line stuff. But most winch applications just use single braid (un-sheathed), such as Amsteel Blue, which is just Samson Rope's brand name for their Dyneema single-braid.
The sheath adds basically zero strength, so no point in using high-dollar fiber for that, it's really just there to make handling easier, and provide some protection to the high-dollar single-braid hiding inside. Try pulling hard on 1/4" single-braid dyneema for 3 hours during a race, and you'll see why they put a braided sheath over the stuff, to give it better grip and more comfortable diameter. None of that matters for winch line, so the sheath is usually skipped, but maybe it shouldn't be when using the line for skidding logs.
I have decades of experience using this stuff for halyards, sheets, and control lines on sailing yachts, but I'm still with old-skool steel cable for my log skidding winch. I suppose you could make most of your winch line out of single braid Dyneema, and then just eye-splice it to something like 20 feet of steel cable at the end, as that's where most abrasion occurs. You don't necessarily need to be all in one camp or the other, especially if you take a little care with turning blocks (snatch blocks) wherever the line needs to go around a tree, etc.
If you do end up going with a sheath, I'd look for one with high wear-resistance and low cost. which may be polyester. It's pretty easy to replace your own sheath, if you learn to splice line (not difficult), so you could in theory re-sheath your expensive Amsteel Blue single braid every few years, and make the stuff last decades. That would also solve the UV problem, as the Dyneema wouldn't see much sunlight if buried inside a polyester sheath.