Guess I'm kinda late to the party. Ah well, not too late, it seems.
Anyways, I'd advise against most Grass-type starters. With Grass types like Liligant, Gogoat, Roserade, Leafeon (yes, Leafeon), Trevenant and Gourgeist, there's not too much of a reason to make a Grass type your starter.
Unless it's Torterra, Seprerior or maybe Chesnaught. Torterra gets a pretty sweet Curse set. Contrary Serperior can sweep if you set up 1-2 Leaf Storms and spam then either that, Wring Out or Hidden Power. Chesnaught has a pretty good stally-set available, but Gourgeist has a much better one, and Chespin can be obtained later.
Charizard could do well with a Dragon Dance set to boost it's decent speed and average attack, it gets a lot of good physical moves, with only a few usable special moves.
Typhlosion's only advantage over Delphox is slightly higher physical defense (though neither is too bulky) and Eruption, which is very unreliable.
Blaziken is OP, especially since it also gets Baton Pass, so I have no hands-on experience with the thing.
Infernape is a less-OP Blaziken with more move variety and-for some reason- a good Specially Offensive set with Nasty Plot.
Emboar actually functions really, really well in Trick Room, though it's not too great outside of that.
Delphox is underrated very fun to play with, at least for me. It has the highest special attack out of all starters, can be given Calm Mind if you go back to E12 or earlier and gets some pretty sweet utility stuff to mess around with, such as Light Screen, Trick Room or Magician.
As for other in-game Fire types, Arcanine is great, Ninetales and Houndoom have good Nasty Plot sets (though no real physical defense to speak of), Darmanitan with some Speed Boost support could take down at least half of (almost) any gym, and I hear people like Camerupt, which would be good in Trick Room, maybe not as good as Chandelure though.
Blastoise gets a lot of variety, but it's focused more on bulk than power, so those moves won't do too much damage. And there's bulkier out there as well.
Feraligatr can do good with Dragon Dance I'd imagine. Aqua Tail, Dragon Dance, Crunch/Superpower/Thrash.
Swampert is great, it's Speed being it's only really "low" stat. With Avalanche, It's also the only starter that gets a Water/Ice attack combo (which has perfect neutral coverage on all but Water types) without going back to E12 or earlier for Ice Beam. Though it can be gotten later.
-I'd say that, if you go back to E12 or earlier to breed, Empoleon is the best Water starter by far. It's not as physically bulky as Swampert, but it's still rather tough. It's also more specially bulky, and it has a Steel typing. It's also got a very good Special Attack stat along with great moves to utilize it (if you go back), among which is Agility, making Speed a on-issue. Just breed Scald (or keep Hydro Pump), Ice Beam and Agility onto it and give it either Drill Peck or Grass Knot and it's good to go. But then again, it's also obtainable later.
Samurott is nothing special on it's own. If you have some Speed Boost-er to Baton Pass him a boost or 2, like Scolipede, then have him use Swords Dance, he's pretty good.
Not covering Greninja since you have said you already have one elsewhere.
Notable non-starter in-game Water-type: Kingler, Crawdaunt, Clawitzer, Azumarill and Kingdra all function great in Trick Room. Although Crawdaunt has access to Dragon Dance, any special attack kills it, Azumarill can also go outside of TR, just set up Belly Drum and spam Aqua Jets or something, and Kingdra (a.k.a. Critdra) can use Agility along with Focus Energy so TR may not be that good for it. There's also the Shell Smash crew's members.
SO! I'd say go for either Torterra, Serperior, Infernape, Delphox or Empoleon.