Dwarven Fighter
Human Paladin
Human Cleric
Human Mage
That's the best party right there if you're planning to go through all three games, and it fulfulls the minimum requirements needed of your party. Only one of the characters cannot gain the maximum level of 20 (the Dwarven Fighter) but he's capped at Level 18, so no worries about that. The level cap for EOB1 is Level 11 for all classes except Cleric, which is 10. For EOB2 it's Level 13.
BTW, you don't need the Paladin, but if (and that's a big if, I haven't found a way to confirm or deny this fact) he has Protection From Evil '10 permanently cast on himself, he pretty much becomes a no-brainer pick, as EOB doesn't play any differently whether you have a good or evil party. Besides, the "won't join a party with Evil-aligned characters" is only used when creating the characters, even if you create the most Evil party in all of Faerun, the Paladin NPC at the end of EOB3 will still join up with you.
With this party, you will need at least one Fighter class with maximum Strength (18/00) in order to overcome a puzzle in EOB3. As for the Thief-only doors in EOB2, use Insal the Quick to get through. Getting through those doors is not vital to complete the game, though.
Class-specific level restrictions only apply to EOB3, regardless of what the manuals for EOB1 and EOB2 tell you.
I advise against using Elven characters in EOB. They get none of their racial bonuses, but they do get the racial penalties of being immune to Raise Dead (which becomes a real problem in EOB2) and having somewhat annoying level caps in EOB3.
The Ranger bonus to two-handed fighting is not worth having him vulnerable in the front ranks. Also, he needs massive amounts of XP to gain levels.
Gnomes and Halflings are pretty much a waste of time if you plan to go through EOB3, as their level restrictions there are pathetic.