When choosing a class of rogue, do you get everything from the initial class and the chosen archetype, or you can only choose one of those? (Can I be Rogue (Thief) 1? Without multiclassing?)
PHB, page 96:
At 3rd level, you choose an archetype that you emulate in the exercise of your rogue abilities: Thief, Assassin, or Arcane Trickster, all detailed at the end of the class description. Your archetype choice grants you features at 3rd level and then again at 9th, 13th, and 17th level.
So the archetype is itself a class feature of the Rogue, which grants you specific class features in addition to the ones you get as a Rogue. However, you can't choose an archetype until you take your 3rd level as a Rogue.
And for Expertise, from the same page:
At 1st level, choose two of your skill proficiencies, or one of your skill proficiencies and your proficiency with thieves' tools. Your proficiency bonus is doubled for any ability check you make that uses either of the chosen proficiencies.
At 6th level, you can choose two more of your proficiencies (in skills or with thieves' tools) to gain this benefit.
All Expertise does is allow you to add twice your proficiency bonus, instead of just your proficiency bonus, to checks made with two skills (and eventually four) that you choose. These have to be proficiencies you already have.
You choose 4 proficiencies at 1st level, then you choose two of those proficiencies to have the benefit of Expertise. Then at 6th level, you choose two more proficiencies that you already have to gain the benefit of Expertise.