I was intrigued by the JPEG compression and I did a small experiment using Gimp 2.6.10 in Windows. Gimp uses libjpeg for JPEG handling.

I made an image with a gradient, antialiased text and two shapes: one curved and one aligned with the pixels. See below:

I loaded the image saved it to JPEG and closed it to make sure the data in memory was not used to save the image. The JPEG settings were 100%, optimized, no smoothing, not progressive, 2x2, 1x1, 1x1 subsampling and Integer DCT. I did this 10 times and the resulting image is shown below:

After 10 open/save cycles the image is basically unchanged from the original JPEG. Taking the difference between #10 and #1 and shrinking the color curve to cover only the part of the histogram showing data shows that the image does change but so slightly than for most purposes it is undistinguishable from the original. As expected the largest changes are around the sharp edges of the text and shapes. See enhanced difference below:

Obviously this will vary with other software implementations and methods but I doubt the differences would be too large while using 100% JPEG quality.

Although JPEG with 100% quality will work well I would recommend PNG. Hard drive space is cheap and with PNG there is no worry that the software you use would use a quality setting that may mess up your images at save time.

FlyerX