Because of the design of the trigger guard, you are almost forced to put your ring and little finger at the back smaller end of the guard. Your middle finger goes down around the "hook". And your index finger goes on the trigger- the front one to shoot the gun. Your thumb should be down along the top side of your index finger, laying along the side of the action, and Not wrapped over the wrist of the stock, or the tang/barrel.
You should get better accuracy shooting this gun if you position the hand so you pulling the trigger BACK, and not up. You don't want your index finger rubbing against the bottom of the stock, above the trigger.
If you can, with your hand,( hand size controls a bit on this kind of position) put the lower edge of your index finger against the inside bottom of the trigger guard, and bring the pad of your fingertip to the lowest part of the trigger. If there is any slack, take that up. To fire the trigger without knowing when it goes off, simply roll or "rotate" the finger towards you, bracing it against the trigger guard, to keep from " jerking " the trigger. With a Set Trigger, this technique should work well for you.
Now, all this is for target shooting. Off-hand shooting at game is a different matter.
IF- a big IF-- you are in position where you see the game before it sees you, and you have not disturbed it, AND, you can use a tree limb, or artificial rest( a walking stick works) to support your rifle, THEN you can probably use this same technique to shoot the rifle in the field. However, if the game is moving or you are in the open, forget the set trigger and shoot the gun. Just make a conscious decision to limit such shots to about 1/2 the range you feel comfortable taking a shot from a rest, using the set trigger. Only daily, off-hand practice( dry fire practice is good for this, too) with your rifle to get used to holding and aiming it while moving to an aiming point( target) will make you a better shot with this gun so that you can take longer off-hand shots and be sure of a good hit, and a clean kill.
Most of us, honestly, just don't have the time in our daily lives to do this level of practicing. " To thine own self be true." Wm. Shakespeare