At the moment I mostly use a Hamax Kiss. It's good because it's a bit bouncy so soaks up some of the bumps and I have a rain cover for it which is very effective. I've also used co-pilot seats and cheep
halfords ones. The co-pilots are great, except for the footwells, which are too short with lousy straps, so they are better for smaller children (the biggest I have carried regularly was 6!)
For luggage, I use a combination of front panniers and bar bag/klikfix basket on my normal bike, which works well - the low panniers are a lot more stable than the basket - I have one for lock and shopping and one for folding potty/spare clothes
. When I use the co-pilot I use a backpack, because that bike doesn't have front racks, which limits my shopping.
I have used a trailer in the past, and they work well, with lots of space for children plus stuff, but they make for a long load, especially when pulled by a child-stoked tandem! You can't always make it across cycle crossings before the lights change, but you get so much attention, it doesn't matter too much
. You do have to merge with the traffic more, but equally, they tend to give you more space. The main problem is storing a trailer - my sister had a double one that had to be collapsed to fit through her front door, so she really didn't use it.