The NIR illumination is probably not needed because daylight is a very consistent source of lots of NIR (although using NIR illumination at night could work well). If your goal is to distinguish healthy plants (weeds) from bare soil, your task is fairly easy. Healthy foliage reflects many times more NIR than most bare soil.
Above: Pure NIR (>720 nm) photo of live dandelion surrounded by bare soil. It's easy to tell what is plant and what is not.
An index (e.g., NDVI) is not needed because a pure NIR photo probably produces more contrast between plants and soil. If you are using a good red filter which passes only wavelengths longer than 600 nm, then the blue channel of those photos could be a rather pure NIR photo. Exposure, focus, and processing might be easier with a pure NIR filter like Wratten 87.
If the soil is not bare, the task could be more difficult because old leaves reflect some NIR. In that case it could help to use an index which compares NIR with visible light.
Above: Pure NIR photo (>720 nm) of the same dandelion before I removed the old dead leaves covering the soil. The contrast is not so great here.
Above: NDVI image of the same dandelion on leaf-covered ground. This image was made from a single photo taken with a long pass filter at 620 nm (so the blue channel captured mostly NIR and the red channel captured both NIR and red).
Although an index like NDVI can be helpful, producing useful NDVI images requires a good filter, good exposure, custom white balance or calibration, and image processing. It has to be done carefully to get better results than you could get with pure NIR photos.