Here how we handled the sleeping... with this advice, take it or leave it
We always held the baby until he was in a deep sleep (would take 25-30 minutes) then would lay him down wherever to sleep. During the day, it was on the floor, in his bouncy chair, or in his basinette. At night, he was in his basinette next to us for the first 6 weeks. However, I moved him to his crib at 6 weeks because he was a very noisy sleeper. Any little noise and I would wake up. Once I moved him, I got some better sleep.
As for "attending" to him, if he woke up either crying or even fussing a little, we picked him up. At that point we would feed or rock him back to sleep and wait the 25-30 minutes for deep sleep to over take him. Then we would lay him back down. Granted, he often took 2-3 hour naps in our arms too when we just wanted some snuggle time. When we did lay him down, he would wake up often... sometimes after just a few minutes and we'd go back to the holding/rocking to get him back to sleep. There were times when laying him down would wake him up no matter what, and during those time, we just held him/slept with him. There were many early mornings that both DH and I would lay in bed propped up with our baby asleep on our chest. Some would argue that this isn't safe, but we were comfortable with it.
Around 3.5 months when he started to be more predictable, we'd lay him down in his crib awake at nap time and most times he would drift off to sleep on his own. If he cried, then we'd rock/soothe him to sleep. Now at 9 months, he goes down for naps and bedtime wide awake, and falls asleep on his own. We also have a fisher price aquarium in his crib that can play music, has lights and bubbles, which has helped to distract him from the idea of mommy and daddy leaving him.
This type of "attachment" parenting is discussed in books by Dr. Sears. For me, I think it helped to build a trusting relationship with our baby. He was sleeping through the night by 5 months for 11 hours straight. Even now, he has the once in awhile wake up in the middle of the night... I just go in pick him up and give him a hug and snuggle for a minute and he relaxes and I can lay him back down again. He must like his crib a lot, because when he wakes in the morning, he'll lay there for a good 45 minutes talking to himself before he gets whiney and wants us to come get him. I don't know we just got lucky, or if it was our "method" that got us a really good sleeper after a few months.
At 4 weeks old, your little one is nowhere near capable of self-soothing. She loves her mommy and wants to be with you! Don't worry about sleeping with her, or always holding her... there will be plenty of time later to change the routine as she gets older and is more trusting of your bond and her environment. As for your comment about getting stuff done, I totally know how you feel! I just tried to remind myself that the baby doesn't care about laundry being done, the dishes washed, or if the house is picked up. But the baby will care if mommy is tired and cranky... so try to sleep when she does and forget everything else except keeping yourselves rested and fed.
Hope some of this helps!
--Julie