When I was asked this on WFLA's Daytime Show I found the wording funny.
How do you decide which extra curricular activities your child should do? Well... you don't. You make suggestions, let them do the same, try them out and then as a family you make a decision.
Doing activities like baseball, football, dance or music is a commitment and usually one that effects the who family.
My son did football for a few years and the commitment was high. Practice was 3 nights a week for two hours a night with games lasting about 3 hours on Saturday. It limited the time the girls could spend doing their activities and it increased the time I spent chauffeuring kids around town.
So before you make a commitment figure out what you want to have them try. What are they interested in? If your child is small and slow sadly football may not be a great option but soccer or baseball may. But if they are twice the size of other kids basketball may seem like the logical idea but maybe they have a song in their heart they need someone to teach them how to play! Don't limit them!!!
If you kid loves to dance but has no rhythm should you keep them from participating? No. Let them dance and realize they may never make the performance team.
All that matters is your kids are having fun, they are safe and you are not going insane.
But also remember once the season or session starts... when you sign up you make a commitment to the coach and team (or teacher and class, etc). Do not just drop out without a very good reason (health, moving, etc). It sets a bad example for your child. Make them stick it out. It shows that they should be able to have people count on them even when it's a sacrifice to themselves, it teaches them responsibility and just because they don't like it at first doesn't mean they won't change their minds.
So sit down, find out your child's interest and try something. It's great for their self esteem and health to find an activity that they are either good at or just plain enjoy. Now if you found something they are good at and enjoy you've hit the jack pot so stick with it!