Hey, NewBrock!
You can get both Bonsly (love the lil' guy!) and Mime Jr. in each game, and what it's referring to is exactly what you're wondering about... their rarity. Bonsly is more common in Pearl, Mime Jr. more common in Diamond. You can still get both, but I believe you will also get them earlier on in the game depending on your version (again, Bonsly for Pearl and Mime Jr. for Diamond).
Starly, Carnivine, Weavile, and Chatot are all available in both versions, with the same chance of appearance. I know all three starters appear in the anime, so if you want all of those, you will have to trade someone... and I happen to have all three so when I've started breeding I'd be happy to hand one of whichever 2 you don't have over.
If you want to know about the appearance percentage of any other Pokemon, and where they appear, look here:
http://www.serebii.net/pokedex-dp/
Just pick the Pokemon you want to know about and it will tell you practically everything you'd ever want to know, including where they are and how often they are likely to appear.
Hope that helped, if you need anything else feel free to ask.
P.S. If you're looking for games close to the anime, Pokemon Yellow was very close to the earlier seasons. Jesse, James & Meowth battle you on occasion, you get Pikachu as your first pokemon, and can get Bulbasaur, Charmander, and Squirtle... even a Lv. 9 or so Pidgeotto, re-creating Ash's own adventure pretty much.