Don't feel bad when gunsmiths say derogatory things about your Handi. I've heard them all myself. They will dispute my effective shots made with Handi's as being impossiable, the gun is too cheap to make those kind of shots. Yea, tell that dead Wolf I shot at 480 yards, or the Fox I hit at 600 yards.
The Handi is capable of shooting 500 and on out to 700 yards, most people aren't. I shoot out to 500 yards all the time with my Handi in 30-06 and 25-06. The 25-06 actually reaches out better than the 30-06. The only thing I have done to both guns is reduce the trigger pull, put an O-ring under the forearm, put a good scope capable of handling a 700 yard shot or farther, then shooting. I have worked up loads, that have the energy to reach out and touch things. 165gr Sierria HPBT for the 30-06, and a Nosler 110gr Accubond for the 25-06. I will not hesitate making a 50 to 500 yard shot with either gun. Both guns will make 700 yard shots, but I don't like the lack of bullet performance after 500 yards. Everything has to be just right or I will pass on the 700 yards shots. Depends on what I am shooting at. A Fox or a Lynx, I'll take a shot on out past 700 yards, they are delicate animals, and easy to kill. A wolf is different they are harder to kill, 500 with the 30 cal and 600 with the 25.
I consider maximum effective range to be where I have a minimum of 2000 fps velocity, and 1000 ft lbs of energy. I carried a .308 for 14 years. It was my only high powered rifle. I shot everything with it, from Antalope to Moose. I started working on shooting at longer ranges, and thought the .308 was it for long range shooting. I killed several Mule Deer at 300 yards and on out to 500 yards. I even shot a Caribou out to 715 yards, finishing it with one shot. Someone else had already shot it and it was getting away, so I took the long shot to prevent a lost animal.
The Handi in .308 will reach on out there, well past 700 yards accurately if you do your part. But your maximum effective range is not near that far for hunting most game animals. Your best bullets are the 125gr MV 3030 fps for a Max Eff Range of 375 yards, and the 190gr MV 2560 for a max Eff Range of 380 yards.
If you are serious about shooting long range, practice practice practice that's the name of the game. Do your home work. Get a chrony and work up your loads to get the Max velocity with an accurate load. Remember your most accurate load may not be the fastest. Check the ballistic coeficient of the bullet you want to use. Then use a ballistic program to determine where your bullet should be at X range. Then go and shoot at that range to verify the bullet is actually there. You will need a range finder, and you will need to learn how to dial your scope or how to use a scope with a range marked reticle. I use both types of scopes. I like the Nikon Ballistic-plex reticle scope, and I also like the Tactical scopes that you dial the range on the turrets. Be aware if you use a scope that has range markings on it, you have to match the scope with your velocity. A scope with a return to zero is a must for dialable turrets. And the manufactor will calibrate the scope for a certain velocity, find out what that is before you buy the scope. It will be in the paperwork that comes with the scope.