I am not interested in hunting because I know its a min. of 10 acres.
Whats acceptable for shooting on private property?
Can I build a private range on my property?
Stipulations?

Local zoning will tell the tale. Contact your town building department. IIRC most towns have a 500' minimum from inhabitated buildings rule as a minimum.

CT General Statute Sec. 53-203 Unlawful discharge of firearms.
Anyone who intentionally, negligently, or carelessly discharges any firearm in a manner likely to cause bodily injury or death to a person or domestic animal or damage property, shall be fined $250 and serve up to 3 months.

No mention of land size or distances, as you can see. HOWEVER, check with your town or city FIRST. They all have their own ordinances.

Many towns/cities have laws against ANY discharge of a firearm within its limits.
Others, like Montville for instance, tried to enact a 500 foot minimum from any dwelling etc.. and it got shot down. I guess there were a bunch of little backyard ranges there.

I personally, have shot on private property in Voluntown, Sterling, and North Stonington, all very rural. I called either the resident state trooper, or the nearest CSP barracks each time too. I was told pretty much each time, "Give yourself 500 feet from your nearest neighbor, have a good backstop, shoot responsibly, and have some respect in regards to how much noise you make, and the times of day you  shoot etc."

All three times, I obviously shot in a direction, away from any house, farm, field with animals etc. I built a solid, and thick backstop, or used natural berms in the lay of the land. I knew what was beyond the backstops/berm. I never have or had any trouble with the CSP or neighbors.

Good Luck!

State law states that you can not HUNT within five hundred feet of a house. The only thing I'm aware of as far as shooting is that you cannot shoot in the direction of any house. Just be aware that every projectile that leaves your barrel is yours forever, you own it. Any richochet that hits a house, an animal, a car, or a person is entirely on you.

In Prospect the State Police have come down a couple of times with some complaints from neighbors and with a proper backstop they said you can shoot all you want but they have to come to the call. Mike

MGP how many acres are you shooting on?