What changed from Classic
Blizzard's September 22 article lists six pairings that Classic did not allow: Human Hunter, Gnome Priest, Dwarf Shaman, Orc Mage, Troll Warlock and Undead Paladin. It sums them up as "new ways to build your character". Tauren and Night Elf gain no class. The article uses Undead where this site says Forsaken, so the table's Forsaken row is Blizzard's Undead row.
Skyborne is the one new race, and the only one on both factions. High Order Skyborne (Alliance) can be a Mage and Windshaper Skyborne (Horde) can be a Shaman; the other four classes are open to both. The Skyborne race page has their racials, and every other race's racials are on its own page from the races guide.
After you pick
Each class name in the table opens that class guide with its talent calculator. Once the pairing is settled, the leveling guide covers the level 60 cap and the zone ranges, and the RestedXP guide sets out what its Forever routes cover if you want one to follow.