Its the start of something new! (My damn keyboard has no music note RAR)
Okay, so Starmie, it turns out, has had both Reflect and Light Screen for a while, and I have seen very little on the subject. Starmie is actually a great 'mon for setting up screens, because of its massive Speed stat and reasonable defenses.
252 HP, 252 Speed, 4 Defense (bulky)
4 HP, 252 Sp Attack, 252 Speed (offensive)
Recover/Ice Beam/Rapid Spin/Thunder Wave
Starmie's Speed, decent defenses, and access to reliable recovery make a good case for its use as a Dual Screener. The obvious screens are there for a reason, while Light Clay lets the screens stay up for eight turns, and Recover allows Starmie to heal up so it can put them up again. Hydro Pump ensures that Starmie does not become Taunt bait. Alternatively, one could use a more offensive set with BoltBeam. What it lacks in power, it makes up in coverage. Or, you could use whatever moves you need to cover threats to your team. Starmie's flexible on attacking options. Other options include the everuseful Rapid Spin, and Thunder Wave, which can slow down switch ins and setup sweepers, allowing you to perform the correct move.
There are now two sets of EVs. The first set allows for maximum durability, which is better for balanced or bulky teams. With this spread, Starmie will be able to switch in and set up screens, then switch out and possibly come back in later to repeat the performance. One should probably use Hydro Pump and a support option. The other spread, as suggested by Shovel, is made for Hyper Offense Teams. With this spread, Starmie will be able to set up immediately, and then begin attacking with more powerful attacks than before, but at the cost of some durability. Ideally, one would use either Hydro Pump and a coverage move, or BoltBeam.
Obviously, this set aims to set up screens and switch to someone who can abuse them. Starmie also can serve as a revenge killer on the side, but lack of investment makes Starmie's attacks easier to take than normal. Starmie's great speed, however, makes setting up both screens an easy job. CB Scizor using U-Turn is only capable of landing a 2HKO after Reflect (66.66 - 78.39%), while CSpecs Chandelure is maxes out at 98.14% damage with Shadow Ball, assuming Light Screen. This guarantees that Starmie will be able to set up both screens before fainting, assuming Starmie outspeeds (likely, due to base 115 Speed) and it isn't any more powerful than CSpecs Chandelure's Shadow Ball. The HO EVs are slightly less bulky, but Starmie will still survive a CB U-Turn from Scizor (barely).
Starmie's job is to relieve stress on set up sweepers and frailer attackers, so they make good teammates for Starmie, being able to abuse these screens to the fullest. Starmie also would like entry hazards removed, as would everyone minus Reuniclus, so Rapid Spin support is nice as well, although not mandatory.
EDIT: Added offensive EVs for a Hyper Offensive set, suggested by Shovel, as well as Rapid Spin and Thunder Wave, as suggested by Shovel and ThePillsburyDoughBoy. Thanks guys!