Water: This is a toss up here, as my favorite of the individual, unevolved starters is Squirtle, but if we're going with the entire line, my vote goes to Piplup, as Empoleon is probably my favorite fully-evolved starter Pokemon. The Water/Steel typing is still one of my favorite to date, since it has very few weaknesses and at least 9 or 10 resistances on top of it.
Fire: After going through each generation, I never really realized how little I care for the Fire type starters until just now. I guess my vote will go to Charmander, since I'm pretty indifferent about the rest of them. I guess I would make Fennekin second, but other than their typing, I can't say I really care for either Braixen or Delphox.
Grass: The Grass type starters are my favorite, and if I were to list out all my favorite starters from 1-18, they'd probably take up 5 of my top 10. My favorite out of all of them though would be Treecko. In fact, the Treecko that I first started with on my Sapphire 10+ years ago is my oldest surviving Pokemon, currently sitting in my HeartGold cartridge.