Most of the parents that I know, how played sports, love it when their kids start to show interest in athletics as well. Most of the time, we ease them or push them into the same games that we played. If you were a football player, than you wanted you son to play football. If you poayed softball than that's what you wanted your daughter to play.
Here's something to think about.
Just because you liked a certain sport doesn't mean your kids will, or that they'll be any good at it. We're all wired differently. Study your child. Some kids like to do it all themselves. They like golf or tennis, or track and field because they know that it falls on them. They do the work. They get the glory or they take the heat, but they like it that way.
Other kids are better in a team setting where they don't have to stand out. They can simply concentrate on playing tough defense on a basketball team and leave the scoring to somebody else. They same for football or other team sports.
They whole idea is not to simply push whatever we liked or did well on them. That may be the way they go, but let them try a lot of different things until they get to be around 14 or 15 and them narrow the field.
When they find out what they're personality and temperment is better suited for, they'll do better.
It's not about us, it's about helping them to find out who they are.
Pick the sport that right for your child.