Most cameras will work for indoor, close-up photography. Most cameras will focus on subjects a few feet away. A typical inexpensive consumer consumer camera (e.g., point & shoot like Canon PowerShot) when properly modified to record near infrared, can probably discern stressed Fast Plants from healthy Fast Plants. A few critical issues are:
Photograph both plants in the same photo to eliminate variation in lighting and exposure.
Use the numerical values for NDVI, not the color of the NDVI image. The standard color look-up tables applied to NDVI images use the same color for a range of NDVI values which obscures subtle differences. Alternatively, you can make special color look-up tables with many colors in the range of NDVI values of interest.
To produce NDVI results comparable with legacy (e.g., satellite) NDVI, the photos should be taken in sunlight or an artificial light with a similar ratio of visible to NIR. NDVI is essentially the ratio of red:NIR reflected from leaves, so if the red:NIR ratio of incoming light is not similar to sunlight, the results will be unique to your setup.
Finding suitable cameras for less than $50 is a challenge and depends on your familiarity with various technologies:
You can buy webcam modules for $5.00 on ebay. Removing the IR cut filter is required. A one-camera system (e.g., with red filter) or a two-camera system (one unmodified, one NIR only) can work.
Clones of Raspberry Pi cameras are available for $5.00 on ebay. Removing the IR cut filter is required. Mastering the Raspberry Pi is required.
Older models of Canon PowerShots are available on eBay for <$20.00. Removing the IR cut filter is required. Good results are possible with one-camera systems example, example (but use a red filter instead of blue). This is probably the path of least resistance to create a sub-$50.00 NDVI camera.