I've uploaded a TIFF and a JPEG of the same image and had them send me a 5x7 of each and I can't tell the difference, even with an 8x loupe. As long as the JPEG has only been saved once or hasn't been recompressed, you should have no problem with the quality.
You have made a key point here. Each time you save a jpeg as a jpeg, it gets compressed again. If you want to test this, open a jpeg and save it as a new name. Close then open the new fileand save again. Repeat about ten times. Compare the tenth saved version to the original. You have just learned about JPEG compression.
So even if you shoot JPEGs, when you copy to the computer and start working on it,first save as aTIFF or PSD to use as your working file. If your ultimate application requires a JPEG, then make a JPEG copy of the final image (which you also have saved as TIFF or PSD).