Good kid photography is probably about 80% skill, 20% gear. Top end gear vs decent gear just makes it a tiny bit easier or gives you better low light flexibility or rarely used features like massive telephoto lenses.
Depending on your portability requirements, a secondhand mid-range DSLR, Sony a6000 series, Fuji T series, RX100, or a good smartphone.
Then the rest is skill- read tutorials, practice, figure out where your shots went wrong, and practice again and again and again. You 100% cannot throw money at equipment and magically take good photos
I know good professional and extremely dedicated and talented amateur photographers who happily, gradually, downsized from full frame DSLRs to their smartphones. They still take great photos.
I also know many, many new parents where the father spends money on fancy new camera gear, takes mediocre photos, then gives up on the camera and also switches to his smartphone. They still take mediocre photos.
Edit: do not buy secondhand to save money. From the questions you asked in your opening post, you clearly don't know enough about cameras to navigate the secondhand market. And also avoid any camera store in TST or any camera store that's on street level with bright neon signage. They are tourist traps.