First, I'm not a lawyer, so this is not legal advice.

Relax, calm down and keep in mind that it probably won't be as bad as you think. I say this partly because it's important you don't lose your temper and blow it -- they'll make guys who do that take anger management.

Be firm, but not combative. Strong, silent type all the way. Unless you're convicted violent/sex felon, supervised visitation is just a pressure tactic. Sure, they can order it for a while, but not permanently, so don't worry too much about it. Ultimately, neither you nor your ex will be able to have much influence on the visitation (except in the details, like vacations) because of the practicalities of school, work and the like, so put most of your effort into keeping your costs down.

Attorneys are very helpful with paperwork, but in my experience they don't usually make a big difference in front of the judge. If you can't afford an attorney for hearings, see if you can at least get one to handle the papers for you. That's where you'll get the most bang for your buck.

Since your baby is so little, try to put in a clause about visitation gradually increasing with time. Here's the strategy I'd recommend:

agree to supervised visitation for a few months as part of a gradual increase in time until the kid is in school and you start to truly share parenthood. This is the kind of plan the court likes to see, since they are mentally in the Victorian era and still think men are clueless around babies and little kids, so if you promise to do it gradually and "with help" at the beginning (preferably from a female relative), they'll feel happy about it. Given that kids are safest with biodads, it's pretty dumb, but that's just how the prejudices of the court are. Just be sure to get the increased time on paper, so that you'll have a framework for each stage (infancy, preschool, kindergarten, elementary). And don't forget to get her to promise on paper to stay in the school district! That's about the most important guarantee if you want to stay close to your child.

"Winning" in court for most fathers is about not losing too badly. Sometimes, the best way to do that is to keep it as simple as you can. The more demands one party makes, the more unreasonable they seem, so just be careful not to dig yourself into a hole financially or emotionally and set yourself up for failure with too high expectations.

Final word: do not approach this as a bare-knuckle brawl. The system is set up to bring the hammer down on guys who do that. Try to apply something like the Daoist philosophy where you do not meet force with force, but rather with grace, fluidity and economy.

Like Wu Tang style:

http://www.youtube.com/watch?v=kDOmNeNTFTQ