Well, I've never played Diablo I but I am a freak for Diablo II.
So here are some of my ideas for Diablo3.
Barbarian/Viking - based on the barbarian from D2. His/her weapons are axes, but can carry all other weapons except staves, wands, bows and the katana. He/she can also throw large and giant swords and axes and pick them up from enemy corpses. He/she can carry a large of giant weapon in each hand.
Paladin/Crusader - based on the paladin from D2 His/her weapons are swords and maces, but can carry all other weapons except staves, wands, bows and the katana.
Hunter/Ranger - based on the native American Indians. He would basically replace the Amazon. His/her weapons are bows and spears, but can carry all other weapons except staves, wands and the katana.
Witch/Mage - based on the sorceress from D2 but with a little added evil. His/her weapons are staves and wands, but can carry all other weapons except bows and the katana.
Samurai/Ninja - a whole new character, based on the Japanese Samurai and Ninjas. His/her weapons would be the katana, short ninja sword, long bamboo sticks and the shuriken. He/she is a master of martial arts and personal combat. His/her only magic powers would be an ability to call upon his ancestors to aid him in battle (a few ghost samurai or ninjas) which would last a limited amount of time, and an ability to increase his attack ability and damage with meditation. He/she is able to carry a katana in each hand due to the low weight of the weapons and can also carry bows.
Druid/Wizard/Shaman - based on the druid from D2 with a few added attractions from the legends of the celtic and briton druids and wizards. His/her weapons are also staves and wands, but can carry all other weapons except bows and the katana.
Necromancer/Dark Lord/Shadow Warrior - based on the necromancer from D2. His/her weapons are wands and staves, but can also carry all other weapons except bows and the katana.
Assasin/Thief/Spy - based on the assasin from D2. His/her weapons are shitchblades, wristblades and daggers. He/she cannot wear metal armour, and has an impressive array of magical and regular traps. His/her distinguishing ability is stealth.
Mercenaries/Bounty Hunters - Another brand new character that consists of two individuals. They can carry and use all weapons and have no magic powers except the ability to ressurect one another (when the survivor gets back to town) if one should die. They are unable to hire anyone else into their party. They would recieve a reward in gold for each accomplished quest.
Now for some general choices when creating characters.
The ability to choose sex.
The ability to choose skin, hair and eye colour.
The ability to choose height, weight, body type and modify it.
The characters can choose whether to ride a horse or walk. A character can ride a horse for a while and then abandon it if he/she wishes to. The horses must be bought. Also they have to buy armour for the horse and shoe it regularly. The horse also has an inventory panel for storing found items. Horses can't enter buildings, but can enter caves, and can sometimes get scared near bosses and throw the rider off.
And one last thing. The ability to put boots, gloves, belts, rings and amulets on the members of your party. They should have an inventory panel.
Don't eat me alive because I've said things that others already have.