None from the get go, each character has their own upgrade item, so you get very little choice on who to upgrade.
I would avoid getting Jake's "Harmful If Swallowed" upgrade in the later difficulties, though. This upgrade lets him swallow up a bunch of non-boss bloons and deal major damage to them. However, it's currently bugged in that that any enemies that were in the attack area, but not actually succed in, become untargetable until he finishes the attack, which is long enough that it can be a death sentence in the hardest difficulty.
I would also avoid getting life regeneration items since they stop mattering when you get to the hardest difficulty.
Other than that, it's common sense (i.e. Don't get more of a specific item than there are characters that can equip it)