A first character should survive mistakes: pulling two enemies, forgetting to drink, running into a patrol. That narrows it to classes with a pet or self-heals.
Easy to learn
Hunter (
Beast Mastery Hunter): the pet holds enemies, you shoot. Aimed Shot is baseline at 20 and traps work in combat now.
Paladin (
Retribution Paladin): plate plus heals. Holy Strike at 6 and Consecration at 20 give you real buttons from the start.
Warlock (
Affliction Warlock): the Voidwalker from the level 10 quest tanks; Life Tap and Drain Life cover most of your downtime.
Save for your second character
Mage: strong, but two melee enemies on a Mage is a corpse run.
Rogue: no self-heal; fights are about openers and escapes.
Warrior: Rage starts at 0 every pull; Victory Rush at 20 helps, but gear matters more than for anyone else.
The Classic or Enhanced preset
Blizzard recommends the Enhanced preset if you're unsure: quest objective areas on the map, one-bag inventory, strafe keybinds (launch post). New players should take it.
Still undecided: which class should I main asks by goal, and the planner builds a plan for one race, class and role.