For Android, I think the best place for you to start would be here, it has a lot of information including standard screen sizes and how to display images while keeping them in the best possible quality.
http://developer.android.com/guide/practices/screens_support.html
I’d also suggest doing as much image manipulation as possible on your server. Images are a pain to work with on Android due to memory constraints and fragmentation. Two phones may store pictures taken the same way with different orientations, and there is no simple way to handle rotations, though it can be done (thankfully, I’ve yet to encounter a phone that incorrectly records Exif data, but I wouldn’t be surprised if they existed…). The more you rely on the phone to do, the more chances you have for error due to manufacturers putting wrappers around and otherwise customizing how it handles media.
As for how to display, ideally if your back end is already doing a bunch of different resizes, you can include your screen density when you request the images and send the best size based on the dev guide. If you want to keep differences to a minimum, at least support med or high density for phones, and extra high density for tablets.
Just my two cents, I’m sure you’ll have a lot of opinions. Good luck.