I really really hope it goes over 4 man. 1 fighter, 1 mage, 1 thief leaves only 1 space for fun. I love role play and 4 man limits this. I love crafting a varied team with non-meta characters/classes, 4 man means precious few slots are taken up. And I dont want DOS style all classes can do everything, I want my fighter depending on the healer, and the mage reliant on the fighter.
Can I ask why you feel you will need those 3 specific classes in your party?
For me, it isn't about specific classes, but roles. For example, you can just as easily swap out the wizard for a sorcerer to fill the role of controller, and some classes like Druid can be build more as a Controller or as a Leader depending upon spell choice. But lacking a role can create some significant challenges. For example, you need a defender to keep your spellcasters safe (be they arcane or divine). You need a leader to make sure that your defender does not fall in combat (either through buffs or healing). You need a controller to make sure that your party is not overwhelmed by shear number of enemies (be it by AOE damage or AOE debuffs). Finally, you need a striker, because you need reliable damage, such as a rogue's sneak attack, a monk's flurry of blows, or a ranger's hunter's mark.
Below are how I personally would sort the various classes by role. Again, some classes can in part fill other roles (paladin's can also be leaders, druids can be controllers, etc), but not in what I would call in an optimal manner.
Controller: Sorcerer, Warlock, Wizard
Defender: Barbarian, Fighter, Paladin
Leader: Bard, Cleric, Druid
Striker: Monk, Ranger, Rogue