Character Classes

Players Handbook (page 19)

Character class refers to the profession of the player character. The approach you wish to take to the game, how you believe you can most successfully meet the challenges which it poses, and which role you desire to play are dictated by character class (or multi-class).

House Rule

The ONLY classes available for player characters are:

• Cleric
• Druid
• Fighter
• Ranger
• Magic-User
• Thief

A Monk is neither applicable to the area where the campaign begins, nor the possible origins of the characters, so it is not possible at this time for player characters to have had any opportunity to become a monk. Or even know what they are.
A Paladin is considered too religious to associate with a group unaffiliated to their own religion, that is makes it incredibly unlikely they would be a player character within a party. They would definitely exist as NPCs, who may join with a group for a specific crusade in their favour, but not in a situation where they were general adventuring. However, take note of the comments re Cleric character class in that they are not as restricted as PHB states and a paladin type of cleric may be possible.
The Assassin is a loner and would not be found in a player character adventuring group. Unless their mission was to kill them all!
The Illusionist (like Druid) does not exist as a distinct character class, and therefore can not be chosen for the player. Some illusion spells will be available to a magic user though.
The Multi-Classed Character is only available for the following races Elf as Fighter-Thief, and Dwarf as Fighter-Cleric.
The Character with Two Classes are not options to start the Aerisian campaign.

Hit Dice, Spell Ability and Class Level Limits

All characters, regardless of the class specifics in the PH, start with d4+6 hit points (ie 7-10). There after they increase in line with the Hit Die Type as per PH p19. See Character Hit Points for additional rules on hit points each level.
There are no class level limits and therefore no maximum hit die. If we get to level 15 and beyond then they get to be super heroes like 5e starts with!
Spell ability restrictions apply as per PH p19.

Armour and Weapons Permitted

If faced with a dragon breathing down on you, and the availablity of an iron shield that your fallen fighter comrade previously had, you as a Druid would not reject the option.
There are NO limitations on armour, shields, weapons, oil or poison. It's up to you to decide if you want your character using these. A thief in plate mail is going to have his detection, movement and subterfuge skills massively reduced by the DM.