Just speaking from my own experience with my two girls, I did a lot better at producing enough milk when I fed on a loose schedule (I mean, obviously if the baby was hungry, I fed her, but I tried to do it at more or less the same times of the day). With my first baby, I was advised to feed her whenever she cried (I swear, this is the kind of crackpot advice they give you at newborn parenting classes in San Francisco)... and that led to her "snacking" - she just wasn't interested in nursing for more than a few minutes at a time, and then would fall asleep (lather, rinse, repeat, every 45 minutes around the clock... UGH!). Well, evidently that wasn't enough for her to get any of the rich hind milk, so she didn't stay full for long, and also my body really wasn't producing very rich milk, because it wasn't called for.
Now, with baby #2, I implemented a loose schedule. Don't get me wrong, if baby was hungry, I fed her, but we tried to keep to the same type of eat/play/sleep cycle at the same time every day. As a result, she was actually hungry when I fed her, and she could drink a TON of milk. She was getting foremilk, hind milk, and all the milk in between. (She looked like Buddha, the fattest baby ever. ;) As a result of the high demand, I supplied a lot more. We kind of got into a routine, and it worked out really well. Usually, I fed her at 6am, 10am, 2pm, and 6pm. She slept from 6pm-6am starting at around 4 weeks, and then would nap from 9-10am, and 12-2pm. Like I said, she was very fat and happy, and my milk supply was much higher than it had been with my first child, where we just never got the demand/supply thing down very well.
Anyway, hopefully that helps! Congrats on your new baby!