Fighter/Paladin/Ranger
At least half your party should be comprised of these character classes. All three classes can use any type of weapon or armor, but a fighter can have additional weapon mastery. Paladins have the ability to detect evil and cast protection from evil, but unlike in pen-and-paper AD&D, they can only exercise these abilities on a limited number of occasions per day. Paladins can also heal two hit points a day per experience level, and can turn undead (as a cleric two levels below the paladin). Rangers get a combat advantage against their racial enemy (and you should select a formidable, often encountered enemy, such as ogres or gnolls), and can move stealthily if they are wearing light armor. Rangers do not, however, get the ability to fight with two weapons at once as they can in pen-and-paper AD&D, but they can charm animals. Finally, both paladins and rangers have to be of good alignment, so if you're feeling malevolent, you'll have to opt for a fighter character.
Mage (Including Specialty Mages)
Mages are the physically weakest character classes, but their powerful spells ultimately make them extremely deadly, and every party should have one or two mage characters. There are also eight specialty mage classes: abjurer, conjurer, diviner, enchanter, illusionist, invoker, necromancer, and transmuter. Specialty mages get an extra spell per level (and they don't have to take it in their specialty area either), but cannot cast spells from their opposing specialty school. The extra spell per level advantage makes specialty mages much better choices than ordinary mages, but make sure you check out page 139 of the manual so that you'll know which spells each specialty mage class is unable to cast.
Thief
Thieves are extremely useful characters in the game, primarily because of their hide in shadows, lockpicking and find/disarm trap abilities. You'll want a thief with your party whenever you're exploring an underground cavern to search for traps to disarm. Thieves are also useful in cities because of their ability to pick the numerous available locked chests and containers. Their ability to hide in shadows and then backstab opponents can be particularly deadly, especially when equipped with speed items that allow them to flee opponents once they are discovered. You'll spare yourself a lot of grief if you have a thief with high find/disarm trap abilities in your party.