Bulbasaur in depth
A frog with a garden
The design was created by Atsuko Nishida, who drew it backwards from the way the story is usually told: she started with Venusaur and worked back until she reached the small creature. Ken Sugimori has explained that the reference for the whole line is a frog, not a dinosaur, and you can see it in the stance, the skin, and the short legs. The dinosaur idea comes from the English name, bulb plus saur, which was invented for Western audiences.
The Japanese name makes for a better joke. フシギダネ combines 不思議 (mystery) with 種 (seed), and sounds exactly like “fushigi da ne”, meaning “that's strange, isn't it?”. The whole line keeps the joke: Fushigisou and Fushigibana.
What it does well and what it doesn't
Its 65 Special Attack and 65 Special Defense are the only decent part of its stat spread, and its 45 Speed condemns it to move last against almost any opponent its size. In a normal playthrough, this matters little: it learns Leech Seed at level 9 and Sleep Powder at 15, and with those two moves a trainer can drain health and put whatever gets in the way to sleep throughout the entire early game.
What you do need to keep in mind is the order in which its attacks arrive. Until Seed Bomb at 18, its best Grass-type attacks are Vine Whip and Razor Leaf, neither above 55 power, so the first Kanto Gyms are cleared through status effects rather than brute force. Power Whip at 33 and Solar Beam at 36 arrive when it's already Ivysaur.
First on the list
Being number 001 has made it the face of the series since 1996, and that has had consequences: it's the Pokémon given away at events more often than any other, the one that opens almost every remake, and the only Kanto starter that begins with a type advantage against the region's first two Gyms. Against Charmander, the easy choice, and Squirtle, the balanced one, Bulbasaur is the one that makes the early game easiest and the late game most awkward: the Indigo Plateau is packed with Ice-, Psychic-, and Flying-types.
In the anime, Ash's Bulbasaur arrived on its own and refused to evolve for seasons, something that the games solve with a press of the B button but that became part of its character there.