That depends on the artist, really. Some people like Copics, others like Prismacolors, and then some like Neopikos. Some artists go all out on getting only the highest quality supplies, while I've seen great artists use a frickin' ball point pen. And then some just go digitally.
Most Japanese artists use Copics, because they are very good at blending. However, they are expensive as hell ($4-8 per marker. It's very rare to find the markers at $4 though!) . If you want to try Copics, buy like 6 of them off the bat, and then play around with them. If you like them, then you can keep buying more. If you hated them, well, at least you only bought 6 and not a whole collection of 72. Here are some tutorials on what you could do with them, brought to you by deviantArt.
EcthelianCartoongirl7For pencils, any pencil will do, really. I've known really amazing artist who use just an ordinary #2 pencil. I personally use a mechanical pencil with .5 lead, because I hate having to sharpen my pencils all the time.
One thing to note though, paper might not seem like such a huge deal, but it's really important. Good paper can make all the difference in the world, especially with markers. Printer paper is okay for sketches and doodles, but it will bleed through if you're using markers. Bristol board is very high quality paper that's also quite thick, so it can take more marker work/pens/etc. Most professional comic/manga artists use Bristol board. However, cardstock, which is almost as thick and much cheaper, is also a suitable substitute.