I have noticed many images online have horrible jpeg compression (visible color bleeding).
if you are using paint shop pro (PSP) you have a few important options over photoshop (PH).

to get your file size down but maintain image quality set *chroma subsampling to none. then your compression could be set to 24 and not see a visible difference.

a 512x512 lossless .png file-- 554kb
a 512x512 lossy .jpg file----- 82.4kb

Still I would recommend all your textures and final images be in saved as .png because it is lossless
screenshots and other non priority images could be kept and/or uploaded as lossy .jpgs.

*chroma subsampling adjustment feature not available in PH