The format options are just different ways of storing and compressing the data. Since JPG is lossy they can impact relative image quality but I think it's so nominal it's usually not worth trying everything to see. They do however impact the file size and the difference can be considerable. Baseline Optimized will generally produce smaller files than Baseline Standard and Progressive will typically be smaller yet. But it depends on the image quite allot. Sometimes Progressive can actually be slightly larger. I put mine on Progressive 5 scan (usually) and just forget about it.
The Preview and Quality slider are the important bits here. Move the option box out of the way, make sure Preview is checked as you have it there and then adjust the slider until you're satisfied with the compression noise that results. At 12 JPeg I believe becomes lossless. Every image will be different. Sometimes a setting of 10 is overkill and sometimes it's not enough. Some images can compress way down to 3 or 4 without much noticeable difference - it just depends on the image and the kind of detail it contains. So, for each image you should probably move that Quality slider around and see if you can get it smaller without causing any adverse affects - or if 10 is indeed going to be good enough.
Is that what you wanted to know or were you looking for a more technical explanation?
Cute kitties BTW! :hug::