What is the difference between the shotgun sports. (skeet, trap, etc.)
Skeet is a short range game where the targets are for the most part crossing shots. Trap is a long range game where the targets are mostly going away from you. Sporting clays is something like golf with a shotgun - a variety of targets and presentations spread out along a course.
What is a choke on a shotgun?
Increasing the choke (muzzle constriction) on a shotgun increases pattern density, therefore extending the effective range.
What is the range of these sport shotguns?
The effective range of a shotgun is limited by pattern density. In the best case an effective (target breaking) pattern can be thrown 75 yards. Most guns peter out at 60 yards or less, depending on choke.
The pellets themselves can travel 300 yards plus, but the pattern is too thin to reliably hit anything.
Is it legal to do on your own property, how much space should I give myself.
(If it's any help, I plan on throwing my own discs, and shooting)
Yes, it is legal, moral and fun, subject to municipality discharge laws. The ideal setup would allow you 400 yards of clearance at any angle the gun might be fired.
What is a good started shotgun.
A good starter shotgun will fit you well, be strong enough to withstand years of high volume shooting, have enough weight to protect the shooter from the cumulative effects of recoil, balance and swing well, have barrel(s) at least 26 inches long and be mechanically simple and easy to operate.
Many types of shotgun fill these needs, but more experienced clay target shooters gravitate to the U/O. Many types of U/O's are available which are designed and specialized for a particular sport.
Sharptail