Which moon clip you use depends on what brass you use. For just range use, you are just as well off to use a speed loader, or load singly. BTW, Speed Beez also makes speed loaders for the 8-shot .357 guns.
If you are going to use the 627 for any type of competition where you will be reloading "on the clock", then moon clips are a must.
It really is trial & error when finding the moon clip/brass combo that works. The 8-shot revolvers, unlike the 6-shot .45 ACP ones, are very picky about what works well with them. The clips need to hold the cartridges rigidly enough that they can be easily aligned with the charge holes but have just a little bit of wiggle to help them self-align. Too much and you'll be taking several stabs at trying to insert them. You will also find that the moon clips work best with shorter cartridges. I'd forget .357 Mags in a moon clip - it'll be like pushing rope. Most shooters that compete with the .357 Mag 627's use .38 Long or Short Colt and a few use .38 Spl.
While I don't have an 8-shot .357 Mag, I do have an 8-shot .38 Super (627-4 PC) and went through trials with four different moon clips to find the ones that work best with my gun & brass. I finally settled on Starline brass with S&W moon clips - which are EDM cut with a split-arm design. Guessing that the vendor is Hearthco.
All of this sounds like a major PITA - which it is - but once you are set-up, you are GTG forever and you'll find that it was well worth the effort.
These comments apply only to the 8-shot revolvers. The 6-shot .45 ACP moon clip guns are a piece of cake. Cutting your moon clip teeth on an 8-shot revolver is like being thrown in the deep-end when learning to swim.
Adios,
Pizza Bob
ADDENDUM: For maximum enjoyment of using moon clips in your gun, a quality loader/unloader is a must. I highly recommend the BMT tool. Expensive, but worth every penny.