we're planning to start a new dnd campaign with my friends and we're a little worried about what class to choose. The group will include three players so we cannot fill all roles. What combination of classes would you suggest in order to make a group capable to survive in a campaign?
I'm going to take a strangely contrary position here.
Don't worry about it. Imposing or even suggesting classes without concomitant system mastery will not produce a good result.
I have found that, in starting a new campaign, peoples abilities to predict what they will and will not like to play are extremely poor. Instead of trying to make decisions for the whole campaign right now, instead, engage in a Level 0 adventure for your first game. Once you've gotten a feel for what classes the players want to play, engage in group character creation to have everyone produce a coherent party. The other benefit of group character creation is that when players inevitably make the wrong choices for their characters (mental-model mismatch is really painful, as I can attest from personal experience), it is very easy to bring in new characters without stretching suspension of disbelief.
Furthermore, any party combination should work, though some will require the party and/or the DM to increase their mental flexibility.
From a jurist's point of view, however, there are a number of exceptional combinations, depending on party preferences.
In no particular order:
My most critical advice: Give players 2 cookies: a minor and a major respec. A minor respec is "redo your current build, but keep your class the same." or "Now that you've played the first session, fix the obvious mistakes." A major respec is "no, this person was this other person all along. Don't think too hard about it." This (peanut butter) cookie should be saved when players realize that they don't like what their current role does and would much rather play a new one. Don't forget to refluff so that the players' desires for mechanics match their desires for flavour. Especially when coming from earlier systems, the affordances provided by each class can change significantly. Few things are as un-fun as watching a bard turn suicidal because the player doesn't want to play a leader.
My suggestions is the following:
Include a leader, a striker and a defender and have everyone think about control at least a little bit. Here is an example of what you can do:
This is some solid party synergy and gives a solid basics kind of feel. If you want to go for more interesting stuff you could skip the rogue and go wizard. I'd say the fighter and the cleric are essential. Then depending on what your DM plans to throw at you should determine your choice between a rogue and a wizard (smaller tougher mobs -> rogue, larger weaker (minion) mobs -> wizzy). If you go wizard you may want to consider a hybrid melee/ranged cleric rather than a true ranged cleric. Or you may want to consider a Warlord rather than a cleric.