For the vast majority of the lace work I do, I use a lacing needle that looks like this:
LACING NEEDLE
The end opposite the blunt-nosed end is hollow, with very fine threads on the inside diameter. You clip the end of your lace into a point and thread it up unto the hollow end of the needle. This creates a "locking" fit that is quite secure. Simply push the needle through the hole, pull it out the other side, and the lace will follow.
These needles are cheap, come in different lengths to fit into tight areas, very quick to get a lace locked into and make it simple to get the lace threaded into the glove.
Every once in awhile, I'll use the common lacing tool we've all seen- the long metal one with a hole in one end and a handle to pull on. I rarely use this because, if your threading the lace through a series of holes, you'll have to take the lace out of the end and reposition it for each individual hole. I use this only when I have a tight spot where the needle might not fit or maybe if I'm just pulling the lace through one or two holes.
Over the years I've picked up the relacing kits offered by Rawlings, the Relacer kit you mentioned and another one produced by Franklin. I haven't seen the contents of the Wilson kit, but might pick one up just for nice carrying case!
Each of the kits I have comes with a lacing tool that is essentially a long wire, bent into a "U" shape. You have to poke a hole through the lace, then thread the wire trhough the hole. Once you do all that, the "wire needles" work pretty well. Getting the lace on the wire is a little more time consuming that the "locking needle". I also found the wire needles to be far less durable, getting slightly bent aout of shape after repeated use. They also provide a less substantial tool to grab ahold of and provide leverage for pulling a lace through a tight hole. But they are a fair, inexpensive alternative.
Each of these kits came with a pair of wire cutters (diagonal pliers) for cutting lace. You can pick up a usable one of those for a buck at a discount store. A good pair of scissors can work equally well, but the small cutting area of the pliers fit into tight spaces better and you can also get more force with them.
Besides that, the kits had various combinations of the the long handle standard lacing tool, replacement laces, glove conditioner, glove oil and an awl for punching leather. And each contained a rudimentary set of basic instructions, each with the cautionary note that when pulling a lace through a hole with a metal tool to pull the lace away from your face or body! Good advice, as I've nicked myself a few times when a stubborn lace suddenly yanks free and the lacing tool was pointing toward me!
Of all the tools and gadgets in the three kits I own, I believe the only tool I'm still using is the wire cutters. I already had a good long handled lacing tool that was better that the ones in these kits. The ones in the kits were rather weak and either bent, broke around the hole where the lace goes through or came loose from the handle.
Besides the locking needle and wire cutters, the other tool I use the most is a small pair of needle nose pliers. These come in handy when removing old laces from a glove, getting ahold of a lace in tight place, or even prying under a lace when the pliers are closed. They can save a lot of wear and tear on your fingers a opposed to pulling out the old laces without a tool.
It's getting late and this is getting long, so if there's anything else you would like to know...ask me tomorrow!