welcome! Weapons are pretty much completely independent of your power in DCUO. Also, once you choose your starting weapon, you can easily learn to use any other weapon with skill points. Most players wind up using all the different weapons at some point over their character's advancement. Most of the powers are pretty close now if you're a new player. Pick whichever one you like. Of the 6 free starting powers none are really bad choices.
If you're a lower CR, or combat rating, you can use a lot of different combinations. One of my favorite things to do is use a lot of DoTs or damage over time along with repeated weapon combos clipped with a burst or refreshing my dots
as a precision ( weapon ) player, powers can compliment your specific weapon choice and play style/tactic development. i use rifle for defensive distance control ( fast retreat while executing high damage weapon mastery combos ), flights swoop to instantly put me in melee range ( rifle has no lunge attack ). i use my powers to root targets at distance, crowd control when im getting swarmed, and shield to rally other players as needed. as LT said above, weapons can be changed easily, whereas changing powers is either starting a new character or spending real money on respec tokens. there is also a good chance that your role ( healer / troll / tank ) weapon may be different than your dps weapon. as a troll i use pistols
It's not so much based on powerset as it is based on role. The majority of Healer and Controller builds are going to benefit from a fast-hitting, rapid combo building, fairly mobile weapon for safe distancing and power recovery. Popular choices are pistols, bow, and handblasters. The majority of Tanks are going to want to be in melee, with fast tap combos that can be squeezed in or clipped with the powers needed to hold agro. Popular choices seem to be one-handed and shield. DPS has a greater amount of versatility, because there are DPS who play at range and DPS who are melee. A short range power set will benefit from clippable weapon combos like one-handed. A longer range DPS powerset like Munitions can benefit from something like bow. Independent of range, precision based DPS trend more towards DW/Bow or Bow/MartialArts using the Weapon Masteries for increased parsing damage.
