I kept my hair long during basic, as most girls do. The girls I've talked to who cut their hair short generally regretted it because it's harder to keep clean and always in your face.
On I-day the guys will eventually be put in one line to get their heads shaved, and the girls get in a different line. I was taken into a room, given a partner, and shown how to do a quick military bun. Then the cadre let us wet down each others hair with a spray bottle and gave us about 30 seconds to put our hair in a bun. They had gel and hairspray if we needed it. I didn't have a problem, but I've heard that if you couldn't put it up or if it was always falling out during basic, you had to get it cut.
This is how I put up my hair:
1) Put your hair in a low ponytail at the base of your head (can't get in the way of wearing a hat)
2) Use your finger to twist the ponytail in one direction until it starts wrapping around the hairband
3) Keep twisting/wrapping until all your hair is swirled around the hairband
4) Put a few hairbands around the bun to secure it.
During basic, I'd run some gel through my hair before I put it up and my roommate and I would spray each others hair with hairspray to keep it there. I never had a problem with it falling in my face. If you need to use bobby pins, you can use as many of those as you need as long as it looks neat.
What to bring:
1) You will be issued a comb and really cheap plastic brush, but bring a better brush if you want. I never felt like I needed one.
2) Hair ties that MATCH YOUR HAIR COLOR. This is really easy if you have brown or black hair, but more of a challenge if your hair is blond, red, etc. If you can't find any that match, do your best. These also tend to go missing, so bring plenty extra. I brought mine clipped to a cheap carabiner so they were easier to keep track of.
3) Bobby pins to control bangs, flyaways, and keep everything looking neat.
4) Hair gel and hairspray. Yeah, hair gel pretty much cements your hair to your head, but no one looks pretty in basic. Believe me, your life is much easier if your hair is easy to put up and stays that way. After basic, you can drop the slicked back look.
I'm not sure about hairnets. If you can't see them and they won't come off when you take off a hat, you might be able to use them. It will probably be up to your cadre.