Alright, joined up again, on the East Continent, I think. What is this "Quickplay" button?
While the "Play" button shows you all your unread messages, the "Quickplay" button shows you only personal messages and orders.
Also, would it be a terrible idea to play a Priest or Infiltrator as my first character? They just look so fun!
You will not be able to play an Infiltrator for a while, as they have relatively high requirements. They can be fun, but also somewhat demanding. If you want to have a good chance of carrying out lots of subversive actions without getting caught, you will need to spend some time (and lots of money!) with that character training at an Academy, till your Infiltration skill (and Swordfighting, if you plan on attempting assassinations) is relatively high.
Priests tend to be a "love it or hate it" kind of class. They tend to have somewhat less to do, mechanically, than the more "normal" classes, at least initially. Their main focus is intended to be the roleplay of the religion they belong to. As they gain in skill, they do gain more options for mechanical actions they can perform (ways to influence the peasantry, primarily).
In general, I would advise playing a standard Warrior as your first character, at least for a while. There's no reason you can't change later, and there's no reason you can't create a second character to experiment with at the same time.