Which Car to Choose?
You can separate RC cars for you and your kids into 3 buckets: starter, advanced, pro.
Starter (Good for kids, but not my favorite)
A nice starter car that kids can drive can be anywhere from $20-30. You want something that moves more slowly than advanced cars so it's safer for young kids to try driving themselves. These are cheaper and so won't feel too bad when your kids inevitably break it, but it has less replaceable parts than the more expensive cars so when it breaks you can't fix the tiny plastic parts. Controls for throttle and steering aren't so great at this price range, sometimes having "digital" controls for steering (left or right but no in-between) instead of variable steering.
We got this "meh" Tecnock RC Racing Car and after a month it was clear that the kids and I loved it but we needed something more, leading us to upgrade a more "advanced" RC car in the next section. But this might be a good choice if you want a cheap way to see if RC cars are even fun for you and the kids.
Advanced (More fun for parents - my favorite)
A fun "advanced" RC car is aimed at the parents with limited driving from kids until they're more experienced (7 yo+). Price range $50-100 with a lot of similarities to more professional RC cars having some servicable parts, but at an affordable price. There are some flaws but it's probably the best bang for your buck.
Our favorite RC car in this category is the DEERC "Sandy Land" model that has everything you need to get started out of the box.
It's not perfect. There are some flaws, for example the "Sandy Land" model has holes in the tires in such a way to allow sand to enter and not exit. The mass of sand accumulating in the tires is enough to slow it to a crawl, you need to remove or otherwise slice open part of the tires to clean the sand out.
Still, this is a solid car and we loved it so much after the first died after a year of intense use we bought another of the same model before upgrading to a more "pro" model below.
Pro (Most fun but complicated - now my favorite after learning about RC cars)
This is a full RC car running from $250 - $350 to start, and can climb from there if you upgrade. After a few years of the other models I was ready for something more. My brother recommended this RTR model from LC Racing, a solid RTR (ready to run) RC car kit. We've been rocking it for at least 2 years now using it about once a week and it's kept up very well with some servicing. After a few months the RC transmitter / receiver combo stopped working, so we got a replacement that was higher quality and now the wireless control distance is plenty far for urban parks and playgrounds. We get sand stuck in the gears (seriously avoid sand even though it's fun, unless you're ready to clean) and I had to disassemble about half of it to clean it out. But the point is, it is serviceable so it should last a long time. These are quite fast vehicles that easily go >20mph with the push of a button. You can't let the kids use this directly, usually I will control the throttle while they do the steering. You can also find advanced controllers with throttle limiting, we haven't tried one yet.
You will also need a charger such as this one. I'd advise you to do research and try one of the other models above first to get a feel for dealing with RC cars before getting one of these. (Alternate store link.)