I seem to go through Infinity Time (though I prefer the in-game term of Gnomiverse) way too much so I will give some enlightenment to the chests:
Good Chesty Chest: Seem to be mainly coins, might get an accessory but I can not guaranteed this as I never got accessories myself. Maybe guaranteed coins, just play more and not get this chest, it does not seem like it is worth 5 stars. I usually yield 2.5k to 5k with this.
Great Tra-la-la Chest (can not fully remember the name): Seem to yield more coins than the Good Chesty Chest. Seem to be just like that chest but with more coins.
Amazing Twiddle Chest: Seem to yield accessories (rare mainly but sometimes Super Rare). People report that you can potentially get a Legendary character piece but it is rare. Can also yield coins as a rather underwhelming reward. Just play to the best chest for a bit longer.
Infinite Infinity Chest: "High Likelihood of a Legendary Piece" (at least pre-patch). It seem the chest mainly give Rare/Super Rare accessories though I think it is intended to have a priority towards Legendary characters pre-patch which is likely a bug or issue (or possibly a design flaw). Have a fair chance to get coins like the Twiddle Chest though it is usually higher.
Do not count on my information, my mind tend to get fuzzy when researching grinding things such as this. If you want me to confirm this further, I can always look back into my recorded plays if you like.