I kept the order given by the game, just be aware that you find the Alarm Clock after the other items.

I personally think that the Star Sash is the most useful item except some very specific level where the mask becomes a necessity as the dog, and your eyes, can only click on so many burglar (whom don't steal anything ? What are those people doing there if it's not to steal your stuff ? Just roar to fear your worker ? WHY !?)

I hope this very small guide will be useful to you, don't hesitate to comment if you used it or felt confused as I did myself ♥