3-4" is the usual first pass depth and 6-8" is the maximum you can get with tillers that I am familiar with.
If you are doing lawn prep, adjust the pH with lime, do your first tilling then add any soil amemdments (manure, fertilizer, more lime, peetmoss, etc) and do the second tilling. Broadcast the seed, pack it down tight and water. To help break down the plant material you tilled and to kill off more of the weed seeds, wait 10 days to 2 weeks between first and second tilling. Or till twice and wait. That gives time for the plants to break down and for the weeds to sprout. Tilling again at that point kills the sprouted weeds and helps give your grass a better shot.
While Mr. Bird is correct in what is commonly done, that doesn't make it right. Those folks typically have real ugly yards, especially compared to someone that created a good 8" base of fertile soil of the optimum pH. You do have to worry about weeds when you start from seed. Products containing 2,4-D are effective at controlling broadleaf weeds and are cheap.
jb