Wow its deja-vu all over again. What is being referred to here and CK has eluded to is that there are two very specific "meta"-rules that are being appealed to here. FYI I use the term meta-rule to help summarize the overall thinking behind many card rulings. I'll try to explain both rules and then explain the answer to your question.
Rule #1:
Question: What does "UP to mean":
It means anything that is NOT 0. Thus if you have a card say Claydol GE which says place up to 2 cards from your hand on the bottom of your deck. That means to move onto the conditional action (drawing to have 6 cards in your hand) you must place 1 or 2 cards on the bottom of your deck.
Rule #2:
Question: If something is in my deck and I've played a supporter / trainer to search my deck am a obligated to find anything.
No, the contents of the deck is not public knowledge therefore as your opponent has no recourse to check your deck to find out whether there truly is the card you are are suppose to find, then you can "fail the search". I've seen people indicate that this is cheating, when this topic comes up. It is not. It is a concept throroughly ingrained in the card interpretation and game play rulings given in the Compendium.
Now taking the HM question in context. Yes you must search for 1, 2 or 3 Basic and as far as I know you don't have to declare a number before you search, but you can fail your search and hence take 0.
Hopefully that's clear.
BTW If you really want clarity sit and spend a couple hours reading the Compendium. Once you've done this you will understand there is only one interpretation for every card, and when its not clear in the text (even if you happen to think its crystal clear and you are wrong), there will likely be a ruling.