Unless the baby is in a carseat, the earliest they should ride is probably 9 months or so. I agree with Nightdiver that helmet weight is an important consideration for biking with babies. Using a carseat is possible with a trailer or a front-loading cargo bike or a Madsen "bucket" bike. There's also the Steco Baby Mee that mounts to a standard rear rack, but I think that solution is more likely to get you noticed by police (assuming you're in a jurisdiction that requires helmets for kids): Steco Baby-Mee child seat support

Once they can sit up, I highly recommend front seats, even if you have to get a new bike with a longer effective top tube to give you more space--they're just so much fun. Rear seat would be my second choice, followed by trailers. Cargo bikes aren't really a "need" until you have two kids.