Skip to the last paragraph for a tl;dr.
I don't have specific numbers, but Olivier mentioned a source that states the following:
Hatch those eggs (2km eggs give around 1k stardust or less, 5km eggs around 1500 or less, and 10km eggs around 2-3k. So don't scoff at those 2k eggs
So long as these are relatively accurate, that means you have the following ratios:
- 2k eggs: up to 500 dust per km
- 5k eggs: up to 300 dust per km
- 10k eggs: up to 300 dust per km
Which would suggest that 2k eggs are the best, so long as you are able to keep one hatching.
Now there are a few other things to consider.
When using a 3-use incubator,the limiting factor in this scenario is number of eggs instead of distance, so the criteria for measuring effectiveness changes. You could put three 2k eggs and get up to 3k stardust... or three 10k and get up to 9k stardust. In this instance, putting longer distance eggs would be optimal.
Another factor to consider is your inventory space. In general, it shouldn't matter except in extreme planning scenariors. You can only carry 9 eggs. If you have 9 eggs already, you lose out on gathering more eggs. If you are going to be walking around a and hitting pokestops, you'll want to open up space, so you should hatch the lower distance eggs first.
If you only have 3 eggs, then a higher distance egg wouldn't be an issue since new eggs have spaces to go into.
Lastly, there's also the factor of the hatched pokemon's strength. I read somewhere that the pokemon in the egg (both the breed and the strength) is determined when you first acquire the egg. [I don't remember and can't find the source. Sorry.] So if you grab an egg while level 5 and don't hatch it until you're level 10, it's probably going to be pretty weak. So if you have just used a lucky egg to level up a lot and received an egg, you may want to hatch that first since it is more to be stronger.
But overall, I have come to the following conclusions. It doesn't really matter what you hatch and in what order, so long as you keep hatching.
Of course there are exceptions if you have a specific short-term goal in mind, but besides that, who cares? You just hatch whatever you need the most at the time, and you'll have to hatch them all eventually!
Here is my priority list for deciding:
- Put 10k's into 3-use incubators if you have them (5k's too if you need space).
- If you need a strong pokemon: Hatch the newest 5k or 10k egg you've gotten
- If you want stardust: Hatch all your 2k eggs
- If you're going to stops for more gear: Hatch all your 2k eggs
- If you're going around gym stomping: Hatch your 10k eggs
This optimizes your egg inventory. Until they allow dropping of eggs, the decision should just be about what your next goal is.