I think the trick to avoiding being overwhelmed with the clothing industry is to start it before you start facing droves of dwarves in worn clothing. It also helps to split it between different resources. I always make my shoes and gloves out of leather, for instance. Pants, shirt/tunic, and cap are usually either wool or pig tail/rope reed cloth. Bags are whichever I have more of on hand, but are usually made of leather.
As for farm space, I usually have one to two 3x5 plots for each textile crop I plan to use. I start with pig tails (and dimple cups for dying). These are usually brewed in the first and second year since I don't have any handy clothes makers. That or I let the plots fallow since caravans can easily bring the fort enough booze to live just fine with only a plump helmet farm to supplement. Once I get enough dwarves, I throw two to three into the clothing industry. Farmers help thresh/mill, but the clothiers will thresh/mill as well at first.
By this point, I'm beginning to move away from leather armor, and that means a ton of leather suddenly gets freed up. I always embark with pigs, peafowls, and cats. If I get lucky and my pack animals are a breeding pair, I keep them around. Most of my leather comes from my pigs and cats. If you can, request some more of whichever animal you want to breed for leather. You can get a good setup for leather pretty easily and it'll allow you to cut back on farm space for cloth. (Leather is just easier, period. Tanning gets done automatically, so one less step to worry about. Well, when your leatherworker doesn't decide to party for a year. OTL)
If I get in a pinch and just need a ton of clothes, I'll start ordering clothes in full leather as well, or buy clothes from caravans. I personally never buy clothes. Just cloth to make my own.
Also, I didn't mention silk here because I rarely have a reliable source of it. In the event that I do get enough, I usually attempt to save it for hoods, and cloaks. Hope this helps some. :3
(P.S. Yes, I don't make socks. I'm a barbarian, I know. My dwarves have feet made of iron and steel. They don't need no stinking socks. The refuse pile stinks enough as it is.)