Children: just set them to grow up to adulthood at age 3 or something. Then at least you'll have peasants instead of children when they arrive young.
If you want to have slow immigrants, you'll need to constantly change your init settings to slowly increase your population cap. Though personally, I don't understand why supporting lots of immigrants is troubling. FPS reasons for not wanting immigrants is very understandable, but just keeping them alive? The extra micromanagement I can understand I guess, but with Dwarf Therapist a lot of the management becomes easier. As for the other stuff:
It isn't an fps issue. First off, as far as I know there is still a very big bug in that underground caverns and civilizations add to your wealth, which is what causes these ridiculous immigration waves.
Let's look at my last fort. I embarked on a cold climate, low vegetation, low trees wasteland with a river running through it. So I am in an area where I am facing limited resources, chosen for that reason. Wood in particular is very limited, despite embarking with a stockpile I knew I'd need to trade to fill my needs just to make enough beds for my dwarves. The amount of wood I can trade for is rather limited, and is far outpaced by 100+ immigrants in a year. I can't even make bedrooms for my dwarves, yet I am still drawing 25 or so a season?
1) Food and booze should be overflowing if you have proper farms and 1~2 skilled farmers.
Sure, but with my water source frozen half the year, minimal native plant life to harvest, and no aquifer it is difficult to get up a tremendous amount of farming easily. When everything freezes over and you get a wave of immigrants that more than doubles your population it can be very taxing on the resources set aside for the season.
3) Equipment - we're ore rich and magma guaranteed in DF2010. If you've got a lot of dwarves around, it's not hard to churn out some solid equipment unless you don't have either steel or bronze on site. Magma forges can be up within 1 season after breaching all 3 caverns.
Making steel or even leather armor for the 15-20 dwarves that become military out of a 30+ wave can take an armorsmith, and a few smelters much longer than one season to accomplish. When another wave arrives before the first is even equipped it starts getting overwhelming.
4) Training - do they all need training? What do you want of them? A large number of dwarves are destined to be grunts that do a lot of hauling and menial tasks (like making booze).
What do I want of them? I don't know, maybe to be dabbling or competent in at least one or two combat skills before I end up being hit with 3 raiding parties of goblins in one raid before my second year ends because my population is almost 100?
Is there no way to adjust immigration waves other than tinkering with population cap every time? If not then that is the method I will follow.