Not going to share my kids' details with the world, and don't yet know the gender of the second one, so let's call them Ichiro and Jiro. My wife is a cautious cyclist, and not very big. She'll just ride her own.
2013 - 2014: City Bike with VO porteur rack
Ichiro 3 - 4: Yepp Maxi baby seat (post mount)
Jiro 1/2 - 1 1/2: n/a
I already have a 'city bike' which I can throw the other items on.
Ichiro 5 - 7: Burley Piccolo trail-a-bike
Jiro 2 1/2 - 4 1/2: Yepp Maxi baby seat (post mount)
summer 2018-2020: Bike Friday Tandem
Ichiro 8 - 10: tandem stoker (or on own bike)
Jiro 5 1/2 - 7 1/2: Burley Piccolo
Pretty much only the BF tandems, the Co-Motion Periscopes, and the Kidz Tandem can take a very small stoker, but the BF takes apart most easily at the best price, though I wish the smaller stoker could go in the front like the Kidz. Here is a link to a BF 5% discount (5% of a $2K tandem is $100). This is my only expensive year...
summer 2021-23 - Bike Friday Tandem
Ichiro 11-13 - draft if you like, but you ride your own bike, kid
Jiro 8 1/2 - 10 1/2 - tandem stoker
Then they discover girls, or boys. Whatever.
It is possible to do the Burley Piccolo first, and Tandem after, and may make better sense. I think this works out better than trailers, or cargo bikes: although the tandem costs some money it is usable for over a decade, or more if I get my wife on it, and while the children are not adolescent they'll ride it with me. Tandems also have resale value.