Just so everyone has the numbers for the discussion:
PC race/class restrictions and level limits from the AD&D1 PHB
Dwarf
Cleric - no
Druid - no
Fighter - 9 (need 18 Strength)
Paladin - no
Ranger - no
Magic-User - no
Illusionist - no
Thief - unlimited
Assassin - 9
Monk - no
Multiclasses: fighter/thief
Elf
Cleric - no
Druid - no
Fighter - 7 (need 18 Strength)
Paladin - no
Ranger - no
Magic-User - 11 (need 18 Intelligence)
Illusionist - no
Thief - unlimited
Assassin - 10
Monk - no
Multiclasses: fighter/magic-user, fighter/thief, magic-user/thief, fighter/magic-user/thief
Gnome
Cleric - no
Druid - no
Fighter - 6 (need 18 Strength)
Paladin - no
Ranger - no
Magic-User - no
Illusionist - 7 (need 18 Intelligence and Dexterity)
Thief - unlimited
Assassin - 8
Monk - no
Multiclasses: fighter/illusionist, fighter/thief, illusionist/thief
Half-Elf
Cleric - 5
Druid - unlimited
Fighter - 8 (need 18 Strength)
Paladin - no
Ranger - 8 (need 18 Strength)
Magic-User - 8 (need 18 Intelligence)
Illusionist - no
Thief - unlimited
Assassin - 11
Monk - no
Multiclasses: cleric/fighter, cleric/ranger, cleric/magic-user, fighter/magic-user, fighter/thief, magic-user/thief, cleric/fighter/magic-user, fighter/magic-user/thief
Halfling
Cleric - no
Druid - no
Fighter - 6 (need 18 Strength*)
Paladin - no
Ranger - no
Magic-User - no
Illusionist - no
Thief - unlimited
Assassin - no
Monk - no
Multiclasses: fighter/thief
* Halflings have -1 Strength.
Half-Orc
Cleric - 4
Druid - no
Fighter - 10
Paladin - no
Ranger - no
Magic-User - no
Illusionist - no
Thief - 8 (need 18 Dexterity)
Assassin - unlimited
Monk - no
Multiclasses: cleric/fighter, cleric/thief, cleric/assassin, fighter/thief, fighter/assassin
Human
All classes unlimited
Multiclassing: none
Quasqueton