I (may) have a party with 3 core players and some people that occasionally chime in. While I'm not expecting too many socialisation / synchronisation problems (see this thread about changing characters in a continuing campaign), I do suffer from not knowing what a good 'core party' would be in 4th ed. I presume one Tank, Healer, Controller setup would be good, but I just don't know.
Based on experience, which (party synergy) build(s) would you suggest?
In my experience, the Controller role is easiest to discard. With the later Player's Handbooks, though, there's more classes that fill a primary role and a secondary role, so any role is up for grabs for discarding.
In smaller groups, I find that choosing a theme for the group - maybe based off power source - can be fun, and then you can build out the roles from there. A particularly fun group can be made of Primal characters. Druids (Controller), Shamans (Leader), and Wardens (Defender) can all be built with Striker as a secondary role, which should fill that nicely. A Cleric (Leader), Paladin (Defender), and Avenger (Striker) party seems like a fun opportunity for righteous smackdowns and roleplaying opportunities.
The group that I've been playing with since the release has been between 3 and 5 players. D&D 4e really is pretty forgiving in the role types. I've been playing in a group with 3 players for the last year. In one setting there are no leaders or defenders. In another setting there is a leader, defender and a striker. What I've found is that the second setting (mixed) the combats are slower as the defender and leader are doing very little damage. At the same time, the combats are easy for the DM to design since the encounters are based around this setting. In the first setting (single), we generally defeat things quickly enough that lacking a defender and a leader hasn't been a huge problem.
I think what defines the game is how well you handle the situation. I'm with digitaljoel in that I hate asking people to choose a class based on a role. They should play a character that they enjoy. Everything after that can be worked out pretty easily. I play a barbarian in the single setting, and I've built myself as a tank. I have taken a bunch of regen and temporary hit point generating abilities. My companions focus on doing lots of damage and then vanishing. We work well together in the group because we fill our roles well. A lack of leader has resulted in us spending gold on healing potions, but these are still used only on occasions when we've misunderstood a "trap" encounter, or just had a string of bad rolls.
tl;dr
4.0 is pretty forgiving, and you should allow your players to choose the character they want to play, not a role that must be filled. All of the roles will generally fill a secondary role. Because of this, you can really work out a game with everyone playing whichever class they want. Although, I wouldn't recommend a 3-defender group that didn't include some fighters.
A leader is the most important role, although I've played successfully without one. Still, the game assumes a leader in terms of damage output math and so on.
Once you've got that down, you can make anything else work fairly easily. I'd say the second most important role is a striker, however; your damage output may be a little bit low given that a third of your party is not focused on damage. Choosing something else won't break anything, again, but it'll slow your combats down.
For the third role, go with whatever. Personally I'd choose a second striker, but that's pretty much personal preference for more damage output, and I wouldn't even try to influence my players by suggesting it.
When balancing three people, you'll want to look a bit further into the functions of the classes, as well. For example, if the first two are a warlord and a barbarian, you're going to be a bit more effective than if you went with a shaman and a sorcerer. Warlords and barbarians have good synergy, because the barbarian will take advantage of the warlord's powers, like the ability to grant basic melee attacks. A shaman tends to like to plant his spirit next to the monsters, whereas most sorcerers will be standing back -- so there's not as much synergy there.
Also, hybrids might be a very good choice here, unless your players are new to D&D 4e. Say, two striker/leader hybrids -- that way you'd have the healing you want, and when that healing isn't necessary they can focus on doing damage.
The Controller seems to be widely accepted as the most "disposable" role. Dungeon's Master has a series of blogs on how to compensate for a missing role in your party, going over each one. You definitely don't want to be short a striker, but you can manage without most of the others as long as you carefully balance the characters you do have in your party. Keep in mind that most classes have a secondary role that they can also serve in when needed.
Any combination can work
Any combination can work, as long as you (the DM) make sure to account for the party's weaknesses.
A party without a leader will generally have to use their standard action to spend a healing surge, and will not be able to heal more damage without magic items. They will also have a harder time dealing with conditions. Make sure you give them enough opportunities to buy or find healing items, and when building encounters, carefully think about how many (save ends) the monsters can deal out.
A party without a striker will deal less hit point damage, so a good idea would be to reduce the hit points of monsters. This is a good idea in general, but more important without strikers (or with weak/unoptimized strikers). I reduce HP for all 4E games that I dm, monsters have 50%-75% of the HPs stated in the books.
A party without defender is actually quite interesting, as they are more vulnerable which makes the fights more dangerous. Don't use too many brutes or soldiers against such a party, because they cannot deal with such large amounts of damage.
A party without controller makes the fights less tactically interesting, in my opinion. The party can deal less conditions to monsters. As focus fire is essential in any D&D edition, it's harder to focus fire without a controller that keeps monsters away from the squishies. Don't make your monsters fight too tactical against a party without controller.
In my own campaigns, I've DMd for 3-6 players in various combinations. My personal favorite is a party of strikers and controllers, with maximally one defender and no leader. This because with the striker and controllers, there are enough squishies to make the party feel threatened, but they can really impact the fight with good thinking and clever tactics.
I feel that the additional healing a leader can hand out tends to make combat longer and reduces the feeling of being threatened. And Defenders can take a lot of damage, but their marking mechanic is not a strong enough incentive for intelligent monsters to attack them instead of the squishies, so it 'forces' me to play some monsters less optimally.
The last thing I want is for my players to have to pick a class based on role. I think each of the classes has enough build options that you could put any party together. The GM may have to adjust somewhat to help the party be successful, but they ought to have more fun playing what they want rather than someone feeling like they have to be the healer... again. In a game I'm playing in, we have 2 strikers and myself, a defender. The GM has compensated by making healing potions more available to us, and we are all having a great time.
You can survive without any particular role, so long as the other party members as willing to help pick up the slack in that area. For example, if you don't have a controller, someone should have some ability to hit multiple creatures in a turn. A party without a defender needs somebody (probably two somebodies) who can go toe-to-toe. Parties without strikers should think twice before taking a Pacifist Cleric. And so on.
Controllers are the easiest role to omit in a pinch (generally because your "blind spot" is dealing with minions, which is easily meta-able from the DMs side). Leaders are the hardest role to omit, simply because there are so few non-leader roles that can do significant healing. Skipping a striker or defender will skew how your combats will go (no defender means you can't hold a point easily; no striker will make combats run longer), but aren't dealbreakers.
The main problem here seems to be the fact that you can't fit in all the roles.
I dispute that this is a problem. I DM for a five-player group, and we have 3 strikers(avenger, sorcerer, ranger) and 2 defenders(warden, fighter). We went up against a group of kobolds(hard encounter, 1st level) and it was insane. Basically the kobold soldiers were stuck next to the warden and fighter, hopelessly attempting to actually damage them, while the avenger hunted up some skirmishers, the sorcerer stood back 10 squares and used Dragonfrost on any soldier that got away, and the Ranger went over and one-shotted the shaman. I think the only damage that was dealt by the monsters was when the skirmisher managed to ambush the sorcerer in the very first round.
