Children get expose to a lot of different activities at school, so a child who is particularly gifted in a general area like music, sport, languages, or mathematics will tend to be spotted. You can then choose to develop this area, or allow them to find extracurricular activities that bring breadth to their lives, not just depth to one area.
I'd be wary of throwing them at everything, just to see whether they're good at it. A better idea would be to pick two or three activities that both you and they would like to go to. Remember that you will also spend a lot of time with the parents at the club, and might even start to get involved with running it. It will be a lot more rewarding if you all enjoy the activity, or are at least willing to help the children practice.
I also think it can be a mistake to push them into things you were good at, or always wanted to do. You should pick extracurricular activities that suit your children's temperament and what you can afford as a family (both in time and money). If your motivation is wrong then your children will pick up and become stressed and anxious about the activity, as they sense that you want something from it that they can't give.
In summary, I think it's a parent's responsibility to give their children access to rewarding and enjoyable activities that develop them as people: physically, socially, and intellectually. That could be extracurricular activities, but it could also be playing with friends in the garden. Pick a few things for your children, but don't get too worried about what they are.