When our kids were little we had a trailer, cargo bike and bike seat since biking was our main form of transportation.
Bike seat is the lowest barrier to entry - pop the kid on and go. It does require some creativity for carrying stuff, but a front basket and some panniers can make it work. Get the kind that attaches to the frame, not one that sits on a rear rack so you still have that rack available for bags. The kids love riding high up. If your bike frame isn’t step through it’s a little harder to get on the bike without kicking your kid in the head, but you adapt.
Trailer is the best for crappy weather and for hauling extra stuff. It’s also a good solution for one parent dropping off and another picking up. The disadvantages are that your kids are back there together in a tiny space and it’s hard to tell when they’re fighting until the fight escalates and they’re beating the crap out of each other. Also, to fit two big kids, you need one of the more expensive ones with good head clearance (e.g. Burly D’Lite). I personally found the trailer really hard to tow once the combined weight of kids + trailer exceeded 100 lbs or so. Finally they’re a PITA to lock up at your destination so if theft is a problem in your area, this is a consideration.
Cargo bike is great, but not the right tool for the job if you’re not using it as your every day transportation. That said, older Xtracycles (especially the converted ones) routinely come up on Craigslist here for reasonable prices ($600-$800). So if you get really into biking or start running out of space, it’s definitely worth looking into.