If you don't have a Water-type Pok mon, Pidgey is your best bet. If you beat Brock, you'll receive the Boulder Badge. Also in Pewter City is a Museum. Go into the building to the right of the Museum and talk to the scientists, one will give you a fossil that you can use later. Along the way you'll face about 8 trainers.
Mt. Moon is basically a big maze in a tunnel.
You'll have to go up and down certain stairs to get out. Zubat, Geodue, and Clefairy. There are also several trainers scattered about that you can beat for cash. You'll also get a chance to take 1 of two rare fossils, if you can beat a particular trainer. This is also the first time you'll meet a member of the infamous Team Rocket, a group of evil Pok mon Trainers.