I'm having trouble getting to the greybeards for the first time. I took 2 routes, one from helgan and one going around the mountain on the north side (came along a giant and like everyone else, I got launched to the moon). Am I supposed to level up and do other quests so I can survive the journey to the greybeards? I so far have done the dragon claw side quest, also, (off topic) what's a quick way to make money?
The easiest way I've found is to start from Riften. There's a lake next to it, and if you follow it west you'll come to the river feeding into it. You can follow this river all the way to Ivarsted, which is at the foot of the mountain you need to climb. Other than a few wolves/ice wolves and a troll (running past him is perfectly acceptable at this point) it's not really that bad. Just make sure you heal up between wolves. There's a few that will attack in quick succession.
You can do two things. One is hire a wagon in Whiterun to take you to the nearest town. Two, just run from the troll, it will give up after a short sprint. You should be able to get there with little trouble. The only real bandit nest is the towers along the way (heading around the top of the mountain). I think you might need to do some other local quests before heading up there.