The answer to your question is No, using versatile weapons with two hands does not disqualify them as monk weapons.
But not because of any reason that made you ask the question, because your whole question is wrong as it's clear from your question you haven't understood the paragraph in question.
The paragraph in question on pg. 78, PHB says (emphasis mine):
At 1st level, your practice of martial arts gives you mastery of combat styles that use unarmed strikes and monk weapons, which are shortswords and any simple melee weapons that don't have the two-handed or heavy property.
Let's look at what that paragraph really says.
The first thing it does is stating that at 1st level a monk has a master of different combat styles using unarmed strikes and monk weapons.
The second thing it does is stating that monk weapons are shortswords and any simple melee weapon that doesn't have either the heavy property or the two-handed property.
That's everything that paragraph states. It simply tells you that monks fight unarmed or with monk weapons and then defines monk weapons as either shortswords or any simple melee weapon that isn't heavy or requires two-hands to use.
Simple melee weapon with heavy or two-handed property = not monk weapons.
Simple melee weapon without heavy or two-handed property = monk weapons.
So what about the versatile property? A weapon with that property just gives you the option to use two hands during an attack for greater damage.
However, in this case whether a weapon has the versatile property or not has no impact on the RAW as it only purpose in this case is to define what a monk weapon is, which is a shortsword or any simple melee weapon without either the heavy property or the two-handed property. Any other properties such as light, finesse, reach or versatile has in this case no bearing on the rules. Nor does how you use said weapon.
5 weapons is correct if you always choose the option with the most weapons. Though this probably isn't the best use of your initial equipment loadout.
You could list them all on your character sheet, but it might be better to note your attack bonus (your strength mod plus your proficiency bonus plus any other bonuses), and your damage modifier (your strength plus any relevant bonuses), and then either write down or remember the die that you roll depending on which weapon you're using.
This is probably easier than writing the same expression down several times with a different die in each one.
There are only limits on what kind of attack you can take with a specific weapon if specified. One such limitation is for two weapon fighting which requires light weapons.
Best Answer
There are no restrictions beyond what is written.
Per bullet 1 you can choose any martial weapon and a shield. Or you could choose any two martial weapons.
Later, per bullet 2 you can choose five javelins. Or you could choose any simple melee weapon.
So your proposed starting equipment of halberd and shield (1a) and quarterstaff (2b) is perfectly legal. If the designers had wanted the starting equipment list to have any further restrictions they could have written those in explicitly; compare with druid, monk, rogue starting equipment, for example.