cry it out/sleep training advice!

With my first son I was a single mom so he slept with me until he was 3. Then it took me about 3 nights to get him to fall asleep in his own room, in his own bed. Now I am married and me and my husband just had a baby! I know it's best to let the baby sleep on its back in a bassinet but he will not sleep, so he is currently sleeping on my chest. He is almost a month old and I want to try getting him to sleep by himself soon since I want it to be just me and my husband in our bed, no co-sleeping this time. I do breastfeed exclusively so I need him close by, but I'm wondering at what age is it okay to let him whine a little to fall asleep. I know as a newborn they need attention whenever they cry which is what I have been doing, but if I picked him up every time he cried we would be up all night! Lol. Any advice or past experiences?