Each charge has its advantages, but as a main attack fire and lightning are far, far better than the ice charge. If you were to choose which one of those works best with DS, it would have to be the lightning charge just because DS's corpse explosion is 50/50 physical/fire.
Personally though, I believe that the most fun can be had using all three charges situationally, though not necessarily fully synergized. If you were to focus on lightning, 20 in CoT, 10+ in FoF would work well, with no extra points in BoI necessary, as the ice charge of Phoenix is useful mainly for freeze time.
RE: NextDelay. NextDelay is a mechanic that prevents certain effects from affecting a target too often in a given period of time. It applies to any NextDelay missile, and the duration is in frames. 1 frame = 1/25 second. For the Assassin, skills with NextDelay associated with them are ShockWeb 25 WoF 4, Blade Sentinal 25, and the second and third charges of CoT and Phoenix Strike 4.
For your character it won't matter much if you're playing solo. (If you're playing partied, other people's NextDelays complicate things.) One situation it would matter a little is if you charged up both CoT and Phoenix and released them at the same time. In that case you'd lose some potential damage output to NextDelay, but it's hardly worth worrying about.
That's probably not very clear. Let me give illustrate what happens...
Let's say you're attacking a single monster, and you've decided to use all 3 charges of CoT on it, releasing both the nova and charged bolt effects, both of which have a NextDelay. Since the monster gets tagged instantly by the nova, he's immune to the charged bolts completely for 4 frames, so there's a good chance he doesn't get hit by them at all.
Now let's say you're doing the same thing, but you're additionally charging up your Phoenix lightning charge. He'll get hit by either CoT's Nova, or the initial lightning strike of Phoenix, whichever takes effect first, but let's say it's the Nova for this example. CoT's charged bolts probably won't do anything to him, same as before. However if Phoenix's lightning curves back around he'll get hit by that, even if though he wasn't affected by it the first time, because more than 4 frames will have gone by since he was hit by the Nova.
If that seems confusing, it is. Though I could probably explain a little more clearly if it's not making sense. Long story short, just stay away from skills with long NextDelay missiles like Sentinal and Shock Web, and you'll be fine.
