A question I am asked when people first convert onto the AT.3. In an extensive (i.e I am old!) flying career I have been subjected to a variety of manufacturer’s products and one thing has been common to them all. At some point you have to fly with either hand. Being ex-Navy I have been lucky to fly aircraft that are not designed solely with economy in mind and it is usual for most military aircraft to be flown with the right hand and have the throttle (amongst other controls) on the left. Many civilian machines (PA28’s, 747’s etc) have the throttle in the middle for pilots that sit in either seat, as it is cheaper (PA28) or easier (747) to put it in the middle. Helicopters are always flown with the right hand, except when you have to swap over to do something that is.
So my answer is this. Whenever you have a throttle on your left, fly with your right hand. Assuming that is your natural hand, you should find it more instinctive. You will have to fly other aircraft with your left hand at some point, whether it is to write something down or to reach across the cockpit to operate a switch. Similarly you will have to fly a PA28 with your right hand at some point, for example when you switch tanks. Either way, think about the ergonomics of your particular aircraft and consider high workload events such as a go-around, and what you will have to do with your hands and in what order. Land with your best hand, but don’t get “handed” unless you intend to stick to one aircraft type.
My left hand is rubbish, by the way!