When I was little, I always picked Charmander because he's a sick fire-spitting dinosaur. Also, it wound up somehow that all my friends bought player's guides that told them to start with Squirtle or Bulbasaur because it was easier to start out with them.
As grass Pokemon go, the Bulbasaur family is one of the strongest in RBY. They are one of the few that will learn Leech Seed; a powerful healing attack that will, coupled with Toxic, leave an opponent weakened considerably while your Pokemon barely lifts a finger. Bulbasaur is usually considered the easiest starter, if only because it's type advantages dominate the first two gyms, while your other Pokemon are just beginning to grow and learn new techniques. Later in the game, many trainers will begin to use Psychic-type Pokemon, which Venusaur is weak to. Fortunately, its Special stat is very high, though difficult to take full advantage of offensively due to it's odd movepool; Venusaur excels defensively.
Squirtle was another favorite starter, able to take full advantage of Geodude and Onix's poor Special stat with super effective water attacks. Unfortunately, the Squirtle family's versatility in the later game is dwarfed by the many other great water-type Pokemon to choose from. It's not that Blastoise is a bad Pokemon, it's that you might want to experiment with a Lapras or Starmie, but already have a substantial water Pokemon on your team. This problem also lies with some flying types, so watch your electric vulnerability. Luckily for Blastoise and its pre-evolutions, it comes with a top-class Defense and Special stat, and being a solid water type it's at a disadvantage to electricity and grass types only. It's movepool is also quite versatile, the largest of the three, with many ice type attacks available (as common with most water types) but also a variety of powerful physical attacks as well. Squirtle is a solid starter, with lots of different options and movesets available, however water is such a common type you may want to dabble in some other options.
Charmander is a difficult starting Pokemon. It not only has a difficult time with the first two gyms, but is generally a slow learner. Once you hit the later game however, Charizard is an imperative asset. It's speed is second to none among the three starters, and while Squirtle and Bulbasaur have safety in Defense and Special, Charizard falls prey to low Defense, and its strength split between Special and Attack. Luckily, Charizard may become offensively very powerful due to it's speed and ability to learn moves like Swords Dance and Double Team. Fire is often a very unique touch to any team, while water becomes somewhat common and mundane. It takes some thinking to pull the out the entirety of Charizard's strength, but once you find it, it can be a very powerful force. Not to mention he's a freaking dragon and looks sweet as hell. Venusaur rhymes with ***** sore, and Blastoise is a fat turtle that will hit you with a super soaker. I may be bias, but I'd rather have a flame-spouting dragon monster.
Either way you go, there are strengths and weaknesses with each choice. What maters most though, is your own personal preference. Who your favorites are and what types compliment each other on your own team. If you have a great moveset for Blastoise, go for it. If you're afraid of psychic types, use Charizard and dispatch them where it hurts. Or pick Venusaur for taking a huge amount of damage and dishing it right back. It's all up to the trainer to make the most of his or her Pokemon.