I'd like to ask about the extension which combines small size and good quality, is it .MozJPEG or Browser .JPEG? Also the one thath has no problem with whatever browser? Thanks in advance
I am expecting to know the most practical one for a wordpress website
MozJPEG is just an improved JPEG encoder, fully compatible with the JPEG standard. So you get regular JPEG files, really, just (usually) compressed better.
A better format, which now is supported basically everywhere, is WebP. I'd recommend using it for now.
You might also want to keep an eye on JPEG XL, though it is not yet supported by default by most browsers.