A drowning chamber works exactly the same as a farm, so once you've got one down the other shouldn't be a problem.
It's pretty common for new players to freak out when waves of migrants start coming in, I know I wouldn't usually let my population get above twenty or so until I got the hang of things.
It's just a little hard to make the transition from constantly micromanaging the original seven to the more abstract approach to a fortress with a large population. Designing efficient workshops and storerooms and the like is also an issue, you've got to think big from the beginning, make wider hallways to handle all the traffic, etc.
You can always set a population cap in the init file if you want to avoid a ton of immigrants, I know they can be pretty distracting while you're still trying to learn the basics, but you'll adjust eventually and start actually looking forward to migrations. I can't deal with just twenty dwarves anymore, it seems like work takes forever to get done. Somewhere around 50-70 dwarves is the sweet spot for me now.
EDIT: Oh and just a tip, all those unskilled dwarves you're complaining about, they can be useful. You could always just turn off everything but the hauling jobs, which means your professionals don't have to waste time lugging furniture back and forth, set them as engravers and have them smooth your floors, or just recruit them en masse to the military and forget about them. It's not like they have to do the job they start off with.
[ July 04, 2007: Message edited by: Solara ]