What’s a good fun class to start with for pve and pvp?
There’s no right or wrong, just subjective. Take a class that u think looks cool 
Can only really give my own experience from pve, and I’ll give at least one from each archetype:
Soldier: Conq
Healer: BS (or PoM)
Rogue: Sin
Mage: HoX (or Demo)
As you can see I am a bit biased towards melees so the classes in () are my favorite casters within their archetypes.
As Mori said though this is subjective. Pick whatever you think looks interesting.
You wont get disappointed with barb except duel vs. Bs, conq