For City of Heroes Blasters, the primary powerset is the offensive set that provides attack powers.
Archery - A very stylistic set with many utility powers, you have to really love the concept of archery to go with this set.Assault Rifle - At release this was an excellent set, but the heavy smash/lethal damage is highly resisted by foes. It has a combination of single target, cone area of effect, and stun attacks.
Electrical Blast - This set has decent single target attacks with one mediocre area of effect. Each attack has a bit of end drain, that sadly ends up being mostly irrelevant. A nice looking set.
Energy Blast - This set is very similar to electrical blast but it has slightly better area of effect damage. Unfortunately, the high amount of knockback in this set makes it very group unfriendly.
Fire Blast - The best area of effect set and also good at single target. It also looks absolutely gorgeous. Burn, baby burn.
Ice Blast - Far and away the best single target set. It has a chain of single target ice attacks that animate rapidly and hit hard.
Psychic Blast - The exotic nature of psionic damage makes this set popular with PvPers.
Sonic Attack - This is a damage and support set, as every attack debuffs the damage resistant of its victims.