Part 1: Races and Classes
Before you even start talking about classes in the Gold Box games, it's probably more important to talk about race. You see, the older versions of D&D were pretty damn racist. Or speciest. Whatever. Point being, some classes are just not open to all races. Even if your race allows you into a class, some races have strict limits as to how far you can go into a class. Stats can adjust this to an extent with extraordinary scores being required to reach the highest levels for non-humans. Some of the limits are low enough to be an issue in the basic game, so it's always relevant. Non-humans are classified as demi-humans, and make one significant trade in exchange for their restrictions.In exchange for level limits and class restrictions, demi-humans have the ability to advance in more than one class at a time. This is slower than advancing in single classes since experience is split between each class, but the benefit is that you get all class abilities at once. A mage/cleric gets both spell types according to their level, for example. Unfortunately, level limits still apply and the experience is still split based on how many classes you start with. The size of this benefit is somewhat reduced, however, as this game allows humans to change class and begin advancing in another class, giving up the benefits of the first class until they exceed that level in their new class. With that said, we'll talk about the races:
Humans
The baseline race. No stat adjustments, and have no limits on levels in any class. Humans are also the only race that can be Paladins. Humans are the only race that can reach the maximum strength stat in the game, and are the only race that can use the dual class option. Humans are thus one of the most popular choices and are usually very widespread.
Elves
Elves are short, slim humanoids with insanely long lifespans, resistance to sleep and charm spells, a bonus to finding hidden doors, a bonus to sword and bow attacks, and the fact that they can't be raised from the dead. There are many communities of elves scattered across the world, and this flexibility is reflected in their class choices. Elves are about the second most flexible race and can do just about any mix of fighter, magic user, or thief. However, they can only reach level 7 as fighters, but can reach maximum level as mages or thieves. Stat adjustments are -1 con and +1 dex.
Half-Elves
Two guesses where these guys come from. Get some of the benefits of both humans and elves. They resist sleep and charm spells (although not as well as a full elf) and have a bonus to find hidden doors. They don't get stat adjustments, but can't be quite as strong as a human. Available classes are Cleric (max level 5), Fighter (max 8), Ranger (Max 8), Magic-User (Max 8) and Thief (no limit). Half elves can multi-class like elves, although they can also fold their Ranger class into multi-classing for some odd variants. The full list of available classes is cleric/fighters, cleric/rangers, cleric/magic-users, fighter/magic-users, fighter/thieves, magic-user/thieves, cleric/fighter/magic-user, or fighter/magic-user/thieves. They are thus extraordinarily flexible, but can only advance so far in most of their classes.
Dwarves
Short, sturdy creatures fond of drink and industry. All dwarves get a bonus to saving throws against magic and poison as well as bonuses against goblin and giant type enemies. Stat adjustments are +1 con/-1 charisma. Available classes are Fighter (max 9), Thief (no limit), and Fighter-Thieves.
Gnomes
Short, slender creatures fond of vegetables and being serious about everything. Gnomes are nearly identical to dwarves and get just about all of the same bonuses. The main difference is that they don't get stat adjustments. Gnomes can be fighters (max 6), Thief (no limit), and Fighter-Thieves. I don't know why you would play a gnome, but it's an option. In the base rules they could also be illusionists, but this game isn't that subtle and doesn't have the option.
Halflings
Short, fat creatures fond of food, drink, and other people's valuables. Halflings are resistant to magic and poison, and get stat modifiers of +1 Dexterity and -1 Strength. They can be Fighters (max 6), Thieves (no limit), and Fighter-Thieves. They make better thieves than Gnomes, simply because of that higher dexterity.
Alright, now that we've got races out of the way it's time to talk classes. We have six available.
Cleric
Clerics are the representatives of the Gods, and for some reason in this game they can only be humans or half-elves. They have access to all spells of a level that they can cast, and are tied to a particular deity for their spells. Clerics can only use crushing weapons, but can wear just about any armor. In addition, they can turn undead and either force undead to run away or destroy them outright. Despite what one would hope, this game isn't sophisticated enough to let evil clerics take control of undead. Alignment is important to a Cleric, but in this game they don't have to choose a deity. Clerics don't vary by alignment in this game and all advance at the same level. If you want to suggest a cleric character then you get to do the research for what deity they worship. Forgotten Realms has way too many deities for me to list them here.
Fighter
All weapons, all armor, no spells. Pretty much self-explanatory. Fighters can attack more than once per round at higher levels, and can have higher strength and constitution bonuses than other classes. Nothing more to see here.
Paladin
The champions of the Gods, Paladins are kind of a hybrid character. They are basically fighters, but get additional resistance to spells and poison, can turn undead as if they were a cleric two levels below their current level, learn some low level cleric spells beginning at level 9, and are constantly surrounded by a protection from evil 10' spell (+2 to AC and hit rolls against evil targets). They can also cure a limited number of HP per day and cure disease beginning at 5th level. Paladins can only reach level 11 in this series, in contrast to the 12 that pure fighters can reach.
Ranger
Another kind of fighter with a bonus against giants, and the ability to cast some very low level druid and magic user spells at higher levels. Rangers get additional attacks slightly slower than other fighters, but have higher hit points early on. This evens out in the end. Rangers can only reach level 11 in this series, in contrast to the 12 that pure fighters can reach.
Magic Users
Magic Users are exactly what you'd expect. There are a lot of sub-groups of magic users throughout the Forgotten Realms, but this is mostly for flavor. In this game all magic users have access to the same spell selections, and require intelligence of a certain point to learn spells. We're going to cap out in this series at Level 5 spells, which means that some of the more amusing options are off the table. Stripped of those complications, magic users are fragile flowers who have to be protected in combat.
Thieves
About what you'd expect. Unfortunately, you can't really do any stealing in these games. Thieves are primarily useful for detecting and disarming traps, and also have the ability to backstab enemies. Most locks that can be picked can also be bashed, so they're not that great for that. Thieves can use swords and leather armor, greatly limiting them in combat. High level thieves (10+) can read magical scrolls, but it's usually easier to have a mage do that.