1) You'll get a ton of answers to this, the most common being "All classes can solo, just play what you want". It really depends on what you are looking for in regards to style. If you want to play a "root & nuke" style you'd go with a heavy caster like a Wizard class. If you want to go toe-to-toe you'd take a fighter class. Sneaky stabby types and bow users are found in the scout classes. I would avoid /most/ priest classes as they tend to solo much slower than the rest of the archtypes, however there are a couple of exceptions to that rule.
2) Most? That's tough. I'd guess it to be either Warrior or Berserker. Maybe wizard too. That's really tough. I'm sure the stat is out there somewhere if someone is willing to do the research. As for the least played class, most definitely the coercer due to the high level of difficulty to play effectively. Coercers take a large amount of patience to unlock their full potential and coercer players have to be fine with dying a lot. Because of this a lot of coercers are abandoned by their creators in favor of an easier character class. There are some awful coercers out there because they aren't an easy class to play well, but a well-played coercer is one of the most valuable additions to any group.
3) I would suggest Unrest for non-RP and Lucan D`Lere for RP preferred.