I would recommend you to to monitor the creation of PCs while discussing the choices taken by the players and explaining the expectations of the game. Try to explain issues instead of simply barring anything that you see as possibly problematic. Overall, the effect you want is not "urgh, that nasty GM told me I couldn't play a pacifist barbarian half-drow, what a jerk" but rather "thank heavens our GM told me how my character concept could be improved to make the game more fun for everyone, me included".
I'm going to address two dimensions of this: the fiction/drama side (personalities, backgrounds etc) and the mechanical (class choices, roles etc).
Fiction and drama
Restricting player characters in terms of their motivations and personalities is perfectly normal and is used to weed out some known problematic combinations. One thing I tend to do is blast the players with some expectations for their characters up-front:
Since this is a co-operative game, you'll have to have a reason to stick together. No one's playing a Chaotic Evil trickster who screws stuff up simply because they can.
Since we're trying to have an adventure here, create a character who has a reason to be adventuring. Don't create edgy anti-heroes who will have to be constantly coaxed to do anything.
This is going to be a combat oriented game. Your character shouldn't be a strict pacifist.
This is going to be a serious game, don't create a joke character.
Tailored to whatever suits your game, of course. The style of the game should match your players' expectations, but some things might be more mechanically hard to change. For example DnD 4e works quite well for both serious campaigns and silly ones, but far better for combat-heavy campaigns than more drama-oriented ones.
This stuff is good to do, because it helps people understand what's expected of their characters and avoids future conflicts (often caused by My Guy Syndrome). However, take the time to explain why anything you'd bar is problematic. Your players will understand.
It'd also be wise to go through expectations mechanics-wise. For example, in DnD, classes tend to have quite well-defined roles in the party: clerics heal, barbarians smash, paladins protect, etc. It's the best to be open and up-front about this to your party too - especially new roleplayers might not be aware how rigid this structure can occasionally be.
Trying to uphold a "one of each type" rule may come naturally after the realization, as the players realize it's smart to have characters of each type, but if it doesn't, many lacking archetypes in class choices can be worked around by the GM. For example, if the party lacks a character capable of healing, you can tag along an NPC healer or give them easier access to healing potions or charms.
Another important concept in some DnD editions is class tiers (for introduction, see What are "tiers", and what tier is each class?). In short, the best tiers tend to be both very versatile and powerful, often able to dominate a lower-tier character even in things the lower-tier class specializes in.
You'll want to avoid pairing a powerful and versatile class with a party of mostly weaker classes, because that makes it harder for other players to get their share of success and will likely make the game feel pointless to them. This is harder to work around, so if you're playing an edition where significant power disparity exists between classes, it might be wise to openly ask players to reconsider if they pick characters of vastly different tiers.
EDIT: However, as pointed out in the comments to this answer, class tiers tend to kick in at later levels of play only. So while a high-level wizard might be able to outdo any other member of their party, this is not likely to be a concern for a long while.