I believe that there was a post about this some time back.
Basically, you have a few options. The ‘best’ in my view is to pick the size your comfortable with (Your phone’s?) and then scale from there.
As for the ratio? The method I understand is to use some sort of ‘border’ system, that will paint a border of some sort on the edges that are outside of the aspect you wrote the game for.
You should always position HUD/GUI/etc in relative terms (for e.g. relative to the edge of the screen) to make your game aspect-ratio-independent.
As for different sizes, this is a design issue. Non-artists and certain programmers might just want to scale the game’s assets, but this is a poor design choice.
“It’s simply not possible to create excellent, detailed icons which can be arbitrarily scaled to very small dimensions while preserving clarity. Small icons are caricatures: they exaggerate some features, drop others, and align shapes to a sharp grid.” All the sizes of iOS app icons
Simply scaling down:
Better practice, re-designing the assets for different target sizes:
Another thing to consider: do you want to support full-screen on desktop?
If you don’t care, then just design your game with a fixed size. The differences between Android/desktop will be minimal.
If you do want full-screen support, you’ll likely need a significant redesign of your game/assets/HUD/layout/etc.
For the latter, consider how web designers strip a desktop website down to a mobile website. They take away superfluous elements, emphasize certain aspects of it over others, etc. You might be able to learn something from these articles: