What is a power build? and...
In general, power build just means your main goal is to do direct damage. One could say that the possibilities are power, condition damage, support, defense and control and builds have varied proportion of those.
In PvP, the strongest mesmer build at the moment is a power build, very strong at burst damage (killing your opponent as fast as possible) and mobility (in particular using portal in organized teams). But there are plenty of builds which are very good, and may actually be even more efficient than this one since this one really shines in organized teams. So since you are beginner, you really should try out things and find what you like.
Sword and pistol are 2 very useful weapons, which you can find in many builds. Sword does not really fit with condition damage, so you can eliminate that, but except for that, suits most playstyles. Pistol is good for both damage and interrupt (another strong point of mesmers). So that leaves you still a lot of possibilities. For PvP, you should probably look at staff or greatsword (GS) for your second set. GS is more focused on damage while staff is more defensive.
For PvE, really anything works in open world, and I would probably advise GS. For structured PvE (dungeons) people usually prefer going melee (short distance from the enemy) using sword/sword, but that do requires some good understanding of the dungeons not to die.
“Mass PvP” is a bit more difficult. Do you mean WvW for example? The “common” mesmer builds are not as good in group fights as they lack support. In WvW group fights, mesmer usually try to single out enemies out of the group and execute them. But there are decent support builds possible, you may just need to tailor yourself a bit more.
I hope this helps. Good luck in your mesmer adventures