I have two main ones:
First off, I always pick the fire starter first time playing through a generation. Other than me just liking the type, my rationale for it is the following.
1. The fire types starters tend to have the best offensive stats of the three, which is very useful in-game where sweepers and bulky attackers are best.
2. Fire types are good against all of the early game bug and grass types, and good against later game ice and steel types, making fire types solid throughout the entire game.
3. Fire's three weaknesses (water, rock and ground) are all covered by grass, while grass and water have weaknesses that require multiple pokemon to cover.
4. In the earlier games, fire types tend to be found much later in the game compared to grass and water types, so getting one at the start is a real boon. Admittedly, more recent games make fire types available as early as the grass and water types.
5. In games with HMs, Surf is mandatory, with Waterfall, Whirlpool, and Dive seeing use depending on the game. If you pick the water starter, you either run the risk of making your starter and HM slave, or have to carry around and extra water type for that role. With the fire starter (and grass starter I guess) that isn't a problem, as there are plenty of solid water types available in-game for you to use.
The second thing I do, when not doing a Nuzlocke or other challenge that limits the pokemon I can use, I always name my starter but nothing else. That is, until I decide a pokemon is worthy of my end-game team, in which I bring them to the name rater then.