Technically it is all one jumbled phase. It is probably a better idea to place items as you go so you have a better idea of what you should do next. In my playthrough I just placed the spaghetti first and then placed the items, since it is a bit harder and therefore more fun.
You are right, and I had the exact same thoughts about the larger ones. That is why the choice is actually a lie. If you don't pick up a certain item, the game eventually forces you to pick it up in the later rounds so you have at least one of each item by the end. I feel a little sorry for deceiving players, but I know people will optimise the fun away and go for the easier options every time if I gave them a real choice. I'm not saying it's impossible to find a way to encourage players to pick up objectively bad pieces, but it's not easy.
Thank you for playing and giving feedback!