Shooting is a great sport for youths and home schooling families. It is one of very few sports where teens compete right alongside of adults, and where we have found the adults to be very warm and welcoming and supportive of youth participation. The picture shows my daughter with the inset showing a 600 yard target in a shooting discipline known as F-Class. The 10 ring is a 6″ diameter circle.
Being competitive at many sports requires more time and effort than our children can really expend given their academic priorities and other interests. However, all three of our teens have become very competitive in the shooting sports by shooting an average of once a week or so beginning at a young age. My daughter is our best shooter and has won or placed in many local, state, and national competitions. We greatly reduced ammo, practice, and transportation costs by providing for an air rifle and air pistols for inexpensive practice at a home range.
There are a number of paths to get your children involved in shooting. A lot depends on the available resources and interests. If you already own firearms and there is a range nearby, a lot of progress can be made with parent directed efforts using the NRA Marksmanship Qualification Program. It’s a blue booklet that shows parents and coaches how to structure practice and shooting efforts for youths to progress and build skills and earn certificates and recognition along the way in a variety of disciplines including pistol, rifle, shotgun, air pistol, and air rifle. You can download the booklet and read about the programs here: http://mqp.nra.org/ You will most likely want to begin with an area for which you already have the equipment and your children have shown an interest.
My daughter has been a better shot than me since she was 7. I’ve beaten her exactly once since then, back in 2012.
A variety of youth programs like 4-H and Boy Scouts and Royal Rangers also have shooting programs. You need to investigate what is available in your area. Project Appleseed offers excellent training in rifle marksmanship that is very cost effective for youths. Most of these are one and two day events. See:http://appleseedinfo.org/index.html A phone call or two will even determine if the program can provide loaner firearms to youths without them (or families with more youths to participate than available firearms.)
Most ranges and shooting clubs have programs and youth events that are open to non-members. I’d begin with internet searches for shooting ranges near you, visit their web pages, and learn about their youth programs. However, by the time ours were teens, they preferred jumping in and participating in the adult programs, which they have always been welcome to do.
F-Class is a subdivision of NRA High Power where matches are shot with a scoped rifle from a bipod at either mid range (300-600 yards) or long range (800-1000 yards). This has been a favorite of our home school students since reaching high school. The mid range matches can be shot with nearly any scoped bolt action hunting rifle, and our home school students have done well with off the shelf hunting and varmint rifles. Shooting at 800 to 1000 yards requires more customized equipment. A list of F-Class match locations is here. A discipline often similar to F-Class is long range precision rifle or field precision rifle which is also shot from the prone position with a bipod and scoped bolt action rifle from 200-1000 yards.
Postal matches are available in a wide array of shooting disciplines for people who want to compete but who find the schedules and locations of in-person matches prohibitive. Procedures vary, but the basic idea is you download the match rules, shoot on your own, and upload or mail in your targets and or score.
If you are concerned about safety, most states offer a free Hunter Education course which focuses on firearms safety. These courses do a great job teaching safety, but are usually offered at locations that do not provide shooting opportunities like schools, churches, and sporting goods stores.
Feel free to post additional questions here if you consider a few avenues but get stuck on some practical detail.
Lots of youths and ladies in the TN State long range championships, where my daughter took 2nd place Junior in F-Open.
biblicaltheologyofscience 
What does shooting have to do with a “Biblical Theology of Science”?
Two things. Accurate use of projectiles has often played an important and essential role in the directive to “be fruitful and multiple, fill the earth and subdue it.” Readers should recall occasions where the Bible records land being taken with the sword and bow.
Second, Scripture records David saying, “Blessed be Yahweh my rock who trains my hands for war, my fingers for battle.” Home schooling is the best way to impart a Biblical outlook on science to students and children. The shooting sports can be a valuable part of that impartation.
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