Get ready for a long-ish answer from a teacher. [name_f]Remember[/name_f] every child is different and will gravitate towards different things so the following is generalized ideas and reasons.
TLDR; non-negotiables are swimming and martial arts / self defense. Choose a team sport for at least a season. Choose at least one creative outlet.
Lets start with the physical activities.
There are two that are absolute musts even if the child doesn’t want to do them: swimming and a martial arts / self defense. These are survival skills. Swimming is an activity that I have literally never heard anyone say is unnecessary so I won’t bother explaining the necessity. Now, martial arts / self defense. It does not matter how safe you think you are or how safe you think the place you live is. Teach your kid to defend themselves. Whenever something bad happens in a “good/safe” place, it’s always: I can’t believe that would happen, that never happens here, if it really happened why didn’t they fight back, etc. Karate and Taekwondo seem to be the most common starting discipline but if you have the option you should choose Jiu Jitsu. Jiu Jitsu focuses more on fighting to and on the ground. Kids are smaller so using that to their advantage is best. Martial arts / self defense isn’t all about physical fighting, defense and offense. It also teaches focus, how to difuse a situation before physical escalation, respect, and self discipline and reliance. Swimming and martial arts / self defense are two no argument, non-negotiables.
Now slightly off topic, if anyone tries to teach your daughter the BS of “he only hits you because he likes you,” martial arts / self defense instills in her that that is indeed BS and she should defend herself accordingly. I despise how adults defend boys hitting girls and teach girls that that is a show of affection but then question why the women didn’t leave the abusive relationship and victim blame. “I hit you because I love you.”
Moving on…
Some other good physical add-ons are gymnastics and dance (I recommend ballet as a base). Gymnastics and dance will help with coordination, how to spin a bunch without feeling lightheaded, etc. In my experience, the kid who can do any sort of flip is automatically the cool kid on the playground and if they can show others how to do it, it’s instant school friends.
Team sports: Soccer/football, lacrosse, rugby, hockey (field and ice), American Football, baseball, basketball, etc. Put your kid in one of these for at least a season. They may show no interest in team sports but once they’re in they may change their minds or dislike the idea less. If nothing else, it teaches them how to work and communicate with a team. If you are worried about a full contact sport like rugby and American football, don’t be. They can do the ones where instead of tackling, the kids remove a flag from their opponents waist.
Honorable Mentions: Archery, fencing, horseback riding.
Archery: hand-eye coordination, learning to respect a weapon, understanding why you don’t point it a certain way.
Fencing: hand-eye coordination, learning to respect a weapon, footwork, quick thinking, learning how to read and anticipate others intentions based on their subtle movements.
Horseback Riding: learning how to respect and take care of animals.
Now to the realm of the Arts activities.
Painting, pottery, etc. is good because kids need a creative outlet.
[name_f]Music[/name_f] can help with hearing and math, plus it’s a language of its own.
Sewing is just a basic life skill that is also a good outlet for creativity and teaches math skills. Same thing with cooking and baking. Life skills plus math and chemistry.
You can also get more intense when your kids are older and do things like glassblowing and metal work.
Another good extra curricular activity is language learning. Explaining this one isn’t necessary. Some others are rock climbing/ boldering, hiking, kayaking, gardening, coding, video making, trampoline/tumbling, activities at the zoo, etc.
Obviously the kid doesn’t have to do all of this at once. [name_m]Just[/name_m] pick one that is accessible time wise and budget approved. If your kid doesn’t like one thing, then go with a different thing. See what programs are available through the schools, community centers, and [name_u]Parks[/name_u] and Recreation programs before diving into the private sector.
See if a program is parent and child or has an adult and kid class at the same time (like Jiu Jitsu) that way you’re both learning something and sometimes knowing that their parent is close by helps ease the kid into doing something new.
One of the biggest factors I see that discourages a kid from an activity, is when the parent does not show an interest. Parents complaining that they have to get up early and go to games on the weekends, not showing up for recitals, not asking questions, giving compliments or showing enthusiasm for the art projects.
I have also worked with kids that need special accommodations, are autistic or on the spectrum. For these kids one may not be able to do dance because the music is too loud, not do a contact sport because touching of any kind is a no-go, not be in a classroom setting because of sensory overload and feeling crowded (horseback riding was a good thing with this one, while pottery was a hard no).
Basically do as much as you can while paying attention to your kids boundaries of “I hate this because of reasons” and “I think I hate this because it’s new and scary.”