Despite the common desire for experienced players to break free of common stereotypical character concepts, I'm a believer that the these stereotypes are fun characters to play, especially for new players. In this section, I discuss many of the common archetypes seen in people's characters.
Average Joe: this typical character is average: good at fighting, but not too smart/dumb, not too wise/foolish, etc. Lots of options available, these types of fighters often make good characters because they're not trying too hard to be any particular archetype. Good if you have trouble making up your mind. Often fighters, just because it's simple, although sometimes are rogues (more options).
The Dark and Mysterious Character: - this character dresses in dark clothes, maybe doesn't reveal her true name, maybe hides her face somehow. Very mysterious. Can be any class, but often see this with fighters and spellcasters.
The Person in Disguise: maybe it's a runaway princess, this character is more than what they seem. Often rogues, but sometimes fighters or spellcasters.
The Outcast: thrown out from among his own people (or sometimes self-inflicted), this character travels amongst strangers, looking for meaning, or maybe a way back home. Can be any character class.
The Youth: young and inquisitive, naive and wide-eyed, this character knows nothing about the world, and it often gets her in trouble. Can be any character class.
The simplest character for new players is the standard fighter. There are very few special rules for fighters, especially at low levels, and as a result, are an excellent fit for people learning the ropes.
Big dumb fighter: big and strong and not that bright, this character can be really fun to play. You never have to come up with clever plans, and you get to smash things with your sword. Taken to an extreme, this leads to the barbarian, for which there is a special class. Dwarven fighters (below) are similar to this archetype.
Swift and nimble fighter: think swashbuckling, rapier-wielding, swinging off chandeliers. This can be fun to play -- typically pretty smart, too. Rogues, another class, is another class choice that is sometimes used for this sort of fighter (not as good at fighting, better skill choices).
Specialist fighter: this is a character that takes some weapon: say a longbow, axe, or some stranger weapon, and spends all their time becoming a master of it. With the right weapon choice, this can be an excellent, flavorful character that is quite formidable in battle (as long as their weapon is applicable, of course).
Noble Good Fighter: a knight in shining armor, never doing anything wrong, rescuing fair maidens, etc. Paladins, another class, are holy warriors that take this to an extreme. Some people find these guys boring. Code of conduct.
Fighter with a Cause: a man driven by revenge or some other burning motivation, this is a character whose actions are all leading to one final destiny: the Cause (eliminating all evil from the world, tracking down the bad guy, whatever). Rangers (another class -- wilderness fighters) have a 'favored enemy' that they get bonuses against, that can help play this sort of character.
Dwarven Fighter: the most common type of dwarf seen as a player character, the typical dwarven fighter likes to swear, drink, and fight with his axe. He is often committed to duty and honor, and strangely, sometimes speaks with a scottish accent.
There are a bunch of fighter-like classes that are good at fighting, but have some other advantages. These are listed here.
Most of these are relatively rules-light as well (not as rules-light as the basic fighter, but still not very complicated.)
Barbarian: raised at the edge of society, usually with strange rules and customs, a barbarian is big and strong, and can rage - giving him bonuses to attacks and defence, with quite a bit less control.
Paladin: this is a holy warrior, a knight in shining armor. Strict code of conduct (do no evil sort of thing), but mighty in battle. At higher levels, gets to cast spells. Gets a special bonded mount.
Ranger: a wilderness hunter, gets an animal companion. Has a favored enemy with benefits in fighting this enemy. Good at tracking.
Rogues get all the skill points. Which means they're good at lots of different things, like climbing, picking locks, finding traps, jumping -- whatever you choose to specialize in. Rogues are also typically stealthy, and get a special sneak attack that they inflict more damage if their opponent isn't looking.
There are a few common archetypes for rogues.
Thief: outside the law, the thief takes what he wants, maybe killing, maybe just stealing. Morally ambiguous.
Treasure hunter: being able to disarm traps and pick locks is good for dungeon crawlers. This is a Bilbo Baggins type character.
Swashbuckler: you can do this as a fighter, too, but rogues often make good pirates, cavaliers, or other swinging-from-the-chandelier type people.
Monk: a martial-arts type guy. His bare hands are registered weapons. Can do unnatural stuff with body, especially at higher levels.
Bard: good at singing, but also can cast spells and fight. Described as a 'jack of all trades'.
Here we get into people who can cast spells. These are complicated characters to run because you have to have a good grasp of the spell lists to make informed decisions about what you can and cannot do. There are several types of spellcasters.
Wizard: the ultimate spellcaster: pure magic is her watchword. Needs to memorize spells each day before she can cast them. Memorizes them from a book she lugs around with the spells written in it. Can do anything with magic, but not so good at healing.
Sorcerer: like a wizard, but instead of studying and memorizing spells, casts them from innate talent. Don't need to memorize spells, but not as powerful as a Wizard.
Priest: serves some specific god, and gets magic through faith. Has a code of conduct proscribed by the god, and has to memorize spells like a Wizard (but here it's called praying, and you don't have a spellbook). Excellent healing magic. Depending on the god you serve, can have quite different flavors.
Druid: like a nature priest. Has special abilities that involve nature: speak with trees, etc. Can change into animal forms.
You can take more than one class at a time, but there are penalties, and the rules for this are somewhat complicated: I wouldn't recommend it for new players.