What's the most useful style of chain gauge?
"Useful" is hard to define for everyone. For me, "useful" tends to mean "has a lot of uses". The very specific chain wear-checking tools you list above are "handy" in that they do one thing and they do it reasonably well. Useful? Well...if you need to do it a lot and/or it is difficult.

But there is a tried-and-true method using a simple tool that many people already own, and which has a lot of other uses: a tape measure or ruler with inch markings. You simply align an inch mark on one side of a rivet, then look at the corresponding rivet 12 full links away. On an unworn chain, the rivet will line up exactly at 12 inches. A worn chain will be more than 12 inches. On most bicycles, you won't even need to remove the chain to do this. And it works with virtually all modern bicycle chains.

Chain wear in general is a bit of a "religious" issue, but a rule of thumb if you must have one is: within 1/16 of an inch, no problem. Between 1/16 - 1/8 of an inch, probably time to replace the chain. Past 1/8 of an inch, you've probably noticed other issues in the drivetrain.

This (along with many, many other chain-related issues) is summed up nicely at Sheldon Brown's site (see 'Measuring Chain Wear', towards the bottom).