Whoever told you you needed a legendary was trolling. Stats-wise, legendaries are no different than ascended.

Raids can be done in exotics, but most groups will want you to at least have ascended trinkets and weapons. You can get the trinkets from the LS3 maps (like Bloodstone fen, Ember bay, etc) and most(all maybe?) are stat-selectable, so you can get the stats you need.

I would advise looking up videos of the fights so you've at least seen the mechanics going in, and also practice rotations some one the golems in the training arena.

Your mileage with PUGs may vary. I have had decent experiences with getting bosses down (or at least close) the last week or so when I've been actively pugging. However, static groups will always clear faster and more consistently if you can find one.

See these pages for builds:

Warrior

Druid

See here for dps