Available classes

Basically all standard official classes are available. The major exception is that Artificer is restricted to the Alchemist subclass only, none of the other, more technological options are available.
Specific changes to class rules are covered in the creation homebrew rules.
UA might be allowed, but needs to be run by me first, and probably I will point you in the direction of an existing class/subclass that does what you're looking for. There are so many options for class and subclass combos that there is almost certainly an existing one that does exactly what you're looking for!
Favored classes: Each species favors a list of classes based on their culture and circumstance, but these are not set in stone, you don't have to pick one that matches your ancestry, and doing so doesn't give you any bonuses. This simply tells you what you're most likely to run into, depending on where you grew up.
Humans: Fighters, Clerics, some Celestial Warlocks. Barbarians and other types of Warlocks are common in the wilds of human territory. Most humans rely on heavy armor, cavalry, and knightly tactics to overcome their deficiencies in size and strength, relative to their Dragonborn rivals, or speed and quickness, relative to their Elven allies.
Elves: Wizards, Rangers, and Rogues. Most elves devote themselves either to the arcane or to scouting and tracking. Elves are not at home on the front lines, and rarely field standard infantry in any capacity, preferring to use a combination of devastating arcane onslaughts and guerilla tactics when pushed into combat.
Dwarves: Barbarians, Paladins, and Clerics. A stout and devout people, the Dwarves call upon the strength of the Great Motherforge in combat in many ways. Sometimes this is in a literal way, as their war priests and holy warriors do, but sometimes the berserkers of the Dwarven kingdom simply use the ever burning fire of the Motherforge as an inspiration to fuel their battle rage.
Halflings: Monks, Druids, and Rangers. As a species whose culture revolves around balance in spirituality and everyday life, Halflings specialize in these classes, but are known to have representatives of every discipline among their number. Quick and adept at camouflage, many a traveler has been tracked at length by Halflings in the wilds without their knowledge.
Gnomes: Fighters, Wizards, and Alchemists. Having been tasked with holding the line against the Orc's borders, with very little help from any others besides Halflings, Gnomes have developed a system of fighting that relies on taking advantage of their natural abilities, most notably their uncanny ability to weave magic and swordplay together in a way rivaled only by some of the more martial minded Elves.
Dragonborn: Paladins, Fighters, Sorcerers, and some kinds of Warlocks. A highly militant species, the Dragonborn have become finely tuned fighting machines through centuries of successful conquest and war. They are fiercely loyal to their god, and believe that their Dragon blood makes them inherently more powerful than their other ancestral counterparts on Ipath, calling upon the dragonblood to weave their magic.
Every species has their share of Bards, but Bards tend to travel, choosing not to settle down in any one place for too long, and therefore rarely have longstanding ties with any particular people or community.