Kids on Bikes
What you need to ride with kid(s)
a bicycle (duh)
kid-sized bike helmet --> Adam liked a Lazer helmet (the exact model was discontinued but they make other good ones, like Lil'Gekko for toddlers) experts like Twowheelingtots and NY Magazine recommend the Giro Scamp and others...consider MIPS for extra protection
child seat of some kind --> most popular is a Yepp seat (also recommended by Wirecutter), we got the Yepp Nexxt Maxi but the original Yepp Maxi is also highly recommended (both are designed for 9 months to 6 years or 40 pounds); they fit on most bikes' rear racks, if you don't have one we liked the straightforward Topeak Explorer rack (in SF, The Bike Connection in SoMa carries both)
Riding with infants?
Many doctors advise waiting until ~9 months to bike with a child, due to concerns that bumps in the road could be bad for infants...we didn't bike with Adam until he was over a year old, but apparently in the Netherlands it's common to bike with infants (often in a car seat). It seems a bit of a double standard since we generally don't think twice about letting infants go in a car down a dirt country road...? I'd probably be comfortable with rides on smooth asphalt, especially if a bike has good shocks.
Cargo (e-)bikes & kids
Almost any normal bike can carry a kid with a Yepp seat, but you may decide to upgrade for the same reasons we did:
less tipsy - as your kid gets heavier, they can upset the balance on a normal bike (especially at low speeds)
easier hills - San Francisco has some gnarly hills, some of which are tough with a kid in the back
faster/longer range - electric assist lets you go faster/longer without breaking a sweat (especially helpful when dropping off kids at school on your way to work)
more storage - cargo bikes let you bring a kid and groceries (or big toys like scooters) on a single trip
Models to check out
Tern GSD - the bike we have (see photo above), the smallest bike that can carry two kids, has smaller (20") wheels so it isn't tipsy (since your kid is closer to the ground) and it's as long as a normal bike despite being able to haul a lot of stuff; the compact SUV of bikes...some people don't like the touchy steering (due to the small wheels) but we like it. Great for city living.
Tern HSD - smaller/lighter/cheaper version of GSD, only carries 1 kid but otherwise has similar design
Tern Quick Haul - very similar size/design to the HSD, but cheaper (both in price & components, see comparison here)
Benno Boost - another relatively-small bike that can carry two kids; compared to the GSD it feels more like a "normal bike" (due to 24" tires) but it doesn't carry quite as much, also has a >20 MPH option. Along with the GSD, very popular at our preschool.
Benno Remidemi - only carries 1 kid but looks like a lot of fun, a bit like a Vespa! ...20" wheels (so similar pros/cons to the GSD/HSD, although Remidemi's are a bit wider), can attach panniers/racks for storage (slightly shorter rear rack than the HSD)
Xtracycle - various "longtail" e-bikes that carry 2 (or even 3!) kids, good if you have more space and want to haul a lot of kids and/or stuff
Radpower - various cargo e-bikes that are cheaper than the others listed here...they're popular in SF but I've heard that they need more frequent maintenance (you get what you pay for?); might be a good option if you're particularly handy
Blix Packa - looks like a GSD knockoff with slightly larger tires; looks worth investigating but could be "cheap" in both senses of the word?
Box bikes - this style of bike is very popular in the Netherlands, so much so that they are a political constituency ("box bike mothers" are Dutch equivalents of US "soccer moms"), very comfortable/stable for kids, hauls a lot of stuff, the nicest ones are made by Riese & Müller...we tried these out but thought they felt too big/cumbersome (both to ride & store). Probably a good fit for suburban families with a garage?
Shops, groups & accessories
The New Wheel - awesome electric bike shop in San Francisco and Larkspur (Marin), very knowledgeable and helpful; they let you do test rides with your kids...their bikes are pretty pricey but they only carry high-quality models that should last you a long time. Their YouTube channel is also helpful for learning about e-bikes.
Rolling Jackass Kickstand - this has an awful name and costs a lot, but if you can afford it, it's worth it if you're regularly transporting kids—it makes the bike super-stable, so I feel comfortable with Adam climbing on/off the bike on his own --> Note: the new "Gen 2" 2021 Tern GSD has an "Atlas" kickstand that supposedly is just as good
San Francisco Bicycle Coalition - if you live in San Francisco, you should join this group that advocates for safer bicycle infrastructure across the City—they do some great work