We didn't have much of a routine for the first 6-8 weeks while I was still mixed feeding because it was hard to tell how much or how little they had fed, even though they were taking formula as well, so it was pretty much everything on demand, feeding, napping, sleeping and the very short playtime stints. They were really windy, so it was a constant drill of breast-bottle-wind-nap over and over again.
I gave up breastfeeding at 8 weeks and that was when we started implementing some form of routine. We fed them every 3 hours to start with, so it was 12am, 3am, 6am, 9am, 12pm, 3pm, 6pm, 9pm..... following the eat-activity-sleep rota, letting them nap on their bouncy chairs during the day and sleeping in cot at night. Then with time, they dropped the 12 am feed after we gave them a big feed at 10pm instead of 9pm and stretched the nights gradually longer (let them wake of their own accord) and we finally moved to 7am, 10am, 1pm, 4pm, 7pm, 10pm until they started weaning.
Now at 6 months, we do 7am (milk & porridge), 11am (lunch), 2pm (milk), 5pm (dinner) and 7:30pm (milk).
Mine were (and still are) big morning sleepers. If it fits in with your own routines, then it's not a bad thing. Even now, they go straight back to sleep after breakfast and don't wake up until 10am to watch CBeebies on BBC2 before lunch. They they have a nap at half 12 and a nap at 3pm. 8am to 10am is when I get my best sleep too as they wake me up a few times during the night for dummies or just for a moan.
Apart from the weaning schedule, we didn't really impose anything too strictly on them and just let them tell us when they wanted to change. We tried it once and it backfired (they stopped feeding properly), so we went back to what they were happy with and it was better then. We also didn't bother bathing them every night either.
Good luck and well done for getting through the first month!! I didn't believe it at the time, but it DOES get better!!