I’m not 100% sure how they work but I know they boost production, except for pigs. So I’d say the animals that give most expensive items the most frequently. Ostriches don’t lay eggs that frequently so I’d definitely say no there. If you need food goat milk might be good to have more of for cheese. Bunny feet if you need loved gifts (not penny!) Plus cloth is more now so even if they don’t give feet then you’re still not loosing out. I never thought fish ponds would accept them. Learn something new every day! If I remember (been a while since I had fish ponds) lava eel roe (aged in preserve jar) or sturgeon roe made into caviar (preserve jar) both great for extra cash. Up to you what you need most. Food, gifts, money.
The easiest way of thinking about them is they double whatever that animal made that day (bar pigs because it doesn't work on them)
If you have a chicken, instead of laying 1 egg each morning it lays 2, which are identical
If you have an ostrich, it lays 2 each week, both on the same day it would have produced one
If you have a rabbit/duck it'll double what you get for that day, that doesn't mean a high chance for rabbit feet, simply that'll you'll get double when you do roll the chance
If you have it on a fish pond that produced say 2 roe, it will give you 4 roe instead (there are additional quirks with fish ponds in 1.6.8 which allow for getting 999s of roe at a time but that's for another, more complex explanation)