Buy a good camera
If you have kids, and ever take photos of them, you should buy a good camera. Full stop.
It doesn't matter to me who you are, what your background, budget or artistic inclination is. We'll talk about good cameras in a second, but suffice to say that your phone (no matter which one) isn't enough.
Phones take incredible photos. Even my iPhone, now several generations behind, takes excellent photos. But the best phone camera in the world only takes a great photo relative to other phones.
Phones of course, are fundamentally limited by laws of physics. A phone camera's tiny lens and a microscopic sensor can only do so much. Phone makers use sophisticated software to help fill in the gaps. This is why you almost always get good results with your phone. They're great at getting average photos almost all of the time. A dedicated camera on the other hand, can get you great photos some of the time.
If you're a parent with kids, you want these sometimes great photos. Don't settle for always average, strive for sometimes great.
Dedicated camera advantages
Dedicated cameras have several meaningful advantages with respect to physics. To start, they have giant lenses and sensors relative to phones. What they lack in sophisticated software trickery, they make up in sheer glass and sensor. A dedicated camera can use its lens to create actual depth-of-field in your photos. A phone has to use software to replicate this, and will often do so poorly.
Impressive as this software is, it's just not the same. The main reason camera phones are able to shoot decent photos most of the time is that they shoot with tiny apertures. Unless you use something like what the iPhone calls Portrait mode, basically everything in the frame of the photo will be in focus. This results in a flat, lifeless photo with no depth-of-field. Dedicated cameras can do this much better, with physics instead of software.
Next, and most importantly, a dedicated camera (even an older one) will have really quick autofocus. You can focus on a specific part of your shot (instead of everything) and create depth-of-field there.
In the end though, a camera is a tool. It's a means to an end, where the end is a great photo hanging on your wall. My walls are full of photos I've taken with my cameras over the years, but I don't have a single iPhone photo among them.
What to buy?
There's a couple of considerations for buying a dedicated camera. Let's get the basics out of the way, as only a few things really matter: — it should be small enough for you to ever want to bring it with you. Almost all mirrorless cameras made in the last 5-10 years should be fine. — the lens should be "fast" in terms of aperture. An f1.4 lens would be amazing, 1.8 or 2.0 also great, anything less than 2.8 should suit you well. Anything above that, keep looking. — brand name doesn't really matter. Find one that speaks to you.
Recommendations
Finally, let's look at some actual cameras, with some actual realities that you might be facing:
If you don't mind spending lots of money: a Fuji X-T3/4/5 with a 23mm 1.4 lens will serve you extremely well. Just buy one of these and you're done.
If you want a smaller option in this price range, get a Fuji X100V. It comes with some compromises, but is an excellent option in a tiny package.
If you want to spend about as much as your new baby stroller cost: Fuji X-T30ii with a used 23mm 2.0 lens.
If you want to spend a bare minimum on a relatively modern setup: Fuji X-T2 or X-T1 with a 23mm 2.0 lens.
If you really, really don't have any money to throw at this: a used, original Canon 5D or 6D. The original 5D was released in 2005, but is still capable of creating truly incredible images. Paired with a $75 50mm 1.8 lens and you've got enough to fill every wall of your house with beautiful portraits.
All of these cameras, even the 5D from 2005 with a $75 lens will create images stunning images. It'll take just a little practice.
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You probably think your brand new iPhone camera is just fine. But it's really not. It takes impressive photos for a phone, but only average photos for a camera. On top of that, it's powered by software, not physics. A decent, dedicated camera will get you results that can be shockingly superior to a moderately discerning eye.
To make my final case: imagine you take 5-10 really good photos a year (not a bad rate, actually). In 20 years time when your kids are all grown up, you’ll have a couple of hundred precious, and I mean absolutely precious, photos to hang and cherish for the rest of your life (and theirs). In this same time you might have tens of thousands of truly average iPhone photos not worthy of hanging anywhere.
Get a good camera.