As has been mentioned elsewhere, you need to be subscriber to post to the galleries, but can, within reason, attach photo files in threads as well.
The technical restrictions for gallery posts and post attachments are different, but I find that if your posts fit within the rules for the galleries things work well.
Jpeg format works well, and is easily recognised and handled by everyone, so for these purposes I would recommend jpegs.
The maximum size of each gallery image is 850 pixels x 850 pixels (i.e. no more than 850 pixels on a side).
Almost all monitors display images at 72 pixels/inch (sometimes incorrectly shown as 72 dots/inch or 72 dpi), so use that as the resolution.
A little simple arithmetic (850 pixels/ 72 pixels/inch = 11.8 inches) reveals that if you use 850 pixels as the target size for the long dimension in your image, your posted photos will expand to a nice big image on most screens.
And the file sizes are nice and small too.
Technically speaking, you can load larger images (up to 3000! pixels on a side) as an attachment, but it doesn't make any sense to do so unless for some reason you want people to be able to download them and print them! As that adds a lot of bandwidth overhead for APUG, by doing so you are more likely to make Sean and the moderators unhappy.