I'm late to this party. You have gotten lots of great suggestions. Here are some clarifications that may help:
1. Rockler Thin Rip jig:
I have one of those Rockler thin rip jigs. I like it and use it on occasion. It anchors in a miter slot. On a few saws, it does not extend far enough to touch the blade. The two saws that I know about with that issue are both jobsite saws. On those two saws (maybe others!), you cannot rip the thinnest strips because of the gap between the fully extended thin rip jig and the blade. I am away on business travel, so I can't check my saw, but I would say that the gap is 1/2 inch or so. IMPORTANT: The problem occurs with the thin rip jig on the LEFT side of the blade and the rip fence on the RIGHT, as you would normally expect to make the cut.
The thin rip jig will also work in the RIGHT miter slot with the fence to the LEFT of the blade. On my saw, I could use it that way to get the thinnest strips. It works, but it may increase the risk of injury, because everything is backwards and you are not used to operating the saw in this way.
2. Kerf size:
Even if you use a thin kerf table saw blade, you will lose a lot of wood to sawdust from the thickness of the blade itself. For every strip you make, you will waste two or three strips worth of sawdust. The advantage is that with a newly sharpened blade, you can get very clean cuts.
If you use a bandsaw, you won't waste much wood, but it will take more work to clean up the cuts.