The solution is for the PCs to experiment with each of the spells to get a better feel for how useful they are during an actual game. Once your players have a chance to experiment a bit with the spells they have available to choose from, the task of deciding which ones are worth picking will be significantly easier. Also, as the DM, you may wish to reward good Intelligence or Wisdom checks made by the PCs during research activities by giving them suggestions as to which spells might prove useful over the course of the adventure. For example, if you're running the Lost Mine of Phandelver, you may wish to reward a player who spends time researching dragons that Green Dragons are masters of poison, so a Protection from Poison spell may be worth the Cleric's time to have prepared.
Because many of the 5th Edition mechanics and spell changes will likely be new for many players who did not participate in the playtest, the Adventurer's League Player's Guide also offers a nice solution to this problem. During levels 1-4 (the first major tier of gameplay) you can rebuild your character at the end of an episode or an adventure. This will allow you to try out low-level spell combinations without fear of being stuck with poor choices. Encourage low-level players to pick spells that sound cool and appear useful but not to fret over making bad choices because at the end of the session they can retcon their choices anyway.
It's worth mentioning that this should be significantly less of a problem for the Cleric, Druid, or Paladin because they each automatically have access to their entire class's spell list. If they wish to change the spells they have prepared, they can do so at the end of a long rest.
Lastly, note that some spells (those with the ritual tag) can be cast as rituals. This means the casting time is increased by 10 minutes (to prevent them from being used in combat), but the spell doesn't use up a spell slot. Bards can cast any ritual that they know. Clerics and Druids must prepare their rituals just like any other spell they plan to cast, but Wizards can use their spellbooks to avoid preparing rituals ahead of time. Warlocks who take Pact of the Tome have an invocation option which gives them the ability to learn every class's rituals in the same way as a Wizard. There is also a feat (Ritual Caster) which can grant ritual spellcasting to the other classes. This too will allow your players to try out more utility spells that may or may not be useful without making them sacrifice more pragmatic options like combat spells.
To sum up the mechanics of counterspell:
If a creature with counterspell available can perceive any spell within range being cast, they can attempt to counter it. They don't need to know what spell it is, or even have it on their class list to make the counter. Based on this, and what I gather from your context, the short answer is: yes the NPC could have cast counterspell.
Let's tackle the issues one at a time with this knowledge:
Issue 1:
The NPC doesn't have to know that a silence spell is being cast. All they need to know is that a spell is being cast at all. Counterspell counters any spell after all. How would they know that a spell is being cast? Because silence has verbal and somatic components. So, as long as the NPC can see or hear the caster casting something, the NPC has the option to counterspell it.
Issue 2:
Yes. It's been established in the Sage Advice Compendium that (emphasis mine):
If a spell that’s altered by Subtle Spell has no material component, then it’s impossible for anyone to perceive the spell being cast. So, since you can’t see the casting, counterspell is of no use.
So, if the NPC can't perceive the spell being cast, then they can't counterspell it. In most circumstances (casting during combat or from a different room) it's up to the DM to determine if the NPC can perceive the casting. But if the DM rules (or is convinced) that the NPC can't perceive the casting, then the NPC can't counterspell. In this case, I assume that the NPC could see you casting, and you were within range, so counterspell would have been a legal reaction.
Issue 3:
It could, though it doesn't have to. There are some optional rules that allow creatures to identify a spell as it's being cast, but those are... well... optional. Unfortunately, the DM just has to make a call on what this particular NPC would do, and stick to it. There is no rule pulling the decision one way or another. It's reasonable for the DM to rule that the NPC would take the risk and not counterspell whatever you decide to cast. But, it's just as reasonable for them to rule that the NPC would assume that any spell you cast is a threat that can't be allowed to pass, and so would counterspell it regardless of what it turned out to be.
Issue 4:
Technically, a creature doesn't automatically know anything about the effect of whatever spell a different creature is in the process of casting. But the rules are, again, silent on this matter beyond that. So, if the group decided that minimizing metagaming is something that they want to strive for, neither they, nor the DM should know what spell is cast before deciding to counterspell. But that is a conversation that you all will need to have as a group. Some groups are more lenient where everyone knows what spells are being flung around. And still others let the players know what the enemies cast, but not the other way around. You all have to decide for yourselves what would be the most fun.
Best Answer
It would hinge on the wizard being surprised
The idea of the wizard being taken aback by an action and not having a chance to react has a mechanical representation in the rules, it's called the surprised state and is part of the initiative rules, but let's cover a few things first.
Firstly, while not explicitly covered either way in the rules, you can take actions (and bonus actions and reactions) out of combat. See What actions/bonus actions/reactions can a character perform out of combat? and Can a Bonus Action be used outside of a combat encounter? for more on the topic. The combat rules, or initiative specifically, are a tool the DM can use when many things start happening all at once (eg. combat).
So, without rolling initiative, all the wizard's conditions for casting counterspell should be met (a creature they can see can be seen casting a spell). If you do roll initiative though, the wizard would still be able to use its reaction unless it was surprised and its turn is after the PC's. Whether it is surprised is wholly up to the DM, but personally I would land on them seeing the PC do this making them not surprised. If they are surprised they would be able to take the reaction to cast counterspell once they'd had their turn (they wouldn't have been able to do anything on that turn).
However, having everyone roll initiative shouldn't be necessary unless the wizard (or any other PCs or NPCs) would follow up on the spell casting (retributive fireball?). Instead, if you're just rolling initiate for one interaction for two participants, do what I do and simplify it to a Dexterity ability check contest. This might be a good tool also for cases like this where the later outcome is heavily depended on the first action. (There would presumably not be any combat if the wizard becomes charmed and I find some players rather jump to conclusions, and swordpoints, once you tell them to roll initiate and that stings for the player who were trying to charm).