JPEG is the defacto standard for images. It has lossy but variable compression which can go from horrible to absolutely unnoticeable compared to the original.
My recommendation if to use nconvert and call it in a loop (foreach for tsch).
The nconvert tool is very powerfull and has a simple syntax. To simply convert and
out the results:
nconvert -q -out jpeg -o
Replace with a number. 100 gives high the highest and so the least compression.
I find 90 is still excellent quality. 85 is where I find it reasonable. Try a few settings
on a single file to see which quality is good enough for you.
You can make your files smaller also by dropping non-image data. Add the -rmeta flag
for example before the input file name. The -rexifthumb flag removes the EXIF thumbnail.
If you do not want to remove all meta data then the -clean flag can be used. You have
to pass it a number to tell it what to clean. Use nconvert -help for the details.