Hi Charlotte
Like Jim I have outfitted my shop with Loc-Line even though it is admittedly expensive, and I have never regretted it. I use a pump with a momentary footswitch so I can interrerupt the flow, but leave the machine running for multiple cuts/grinds. I use a pump in a bucket since I have no fresh water source in my garage. I split off from the pump with one of the Loc-Line manifolds to go to: MK100 (large tile saw), glass grinder, a homebuilt lapidary-style drum sander with with 8" and 6" drums (2 separate water feeds), a modified Gryphon wire saw, and a pneumatic 4" grinder with center water feed. So the same pump and footswitch feed all the tools. Unless the tool needs full-force water, I like to use 2 shutoffs in line for each tool. One to "set and forget" at a reduced flow appropriate to the tool, and one strictly used as an on-off shutoff. That solves the problem of getting just the right flow repeatedly for a particular tool. Depending on the tool, you may be able to get away with a gravity feed rather than a pump if that is more convenient, but that might not be practical for a tile saw whch needs more water than other tools.
You have not specified whether you are using tap water pressure, submersible pump or gravity. Most tile says have submersible pumps that are switched by the tile saw itself by way of a switched outlet. In this case you won't need a shutoff at all.
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Loc-Line's site is more informative than your supplier's, IMO.
The basic piece you need is the 13" hose kit. The 1/4" will work for your purposes. If you are ingenious at clamping it onto your tool somehow that might be all you need. You can drill a hole in the flat protruding metal from a standard screw-tighten metal hose clamp and mount with that. Or you can see the clamps Loc-Line offers if it looks like you will need that. You will have to determine if 13" is enough to mount and get water where you need it. You may need the "Extended element with clamp" (straight tube) to help mount it. The assembly pliers are helpful but not absolutely necessary.
Depending on the physics involved you might want to get a 90 degree angle sprayer or whatever sprayer seems appropriate, just make sure it's all 1/4" size. You can also use a Y and spray both sides of your blade/work too.
You'll need to attach your supply tube to the Loc-Line. I make that work in various ways, usually well-placed hose clamps from the hardware store will work, but Loc-Line sells fittings to get to just about any plumbing situation you might have.
Happy cooling
Phil