Members of the armed forces of a country other than Canada cannot exchange an armed forces driver's license or permit for an Alberta driver's license of an equivalent class. You must change a valid driver's license from your home state or country. When you move to Ontario, you can use a valid license from another province, state or country for 60 days. After 60 days, you must change to an Ontario driver's license.
Alberta Health requires proof that you are an Alberta resident, either a government-issued ID or a copy of your utility bill, etc. There is no harm in obtaining an Alberta GDL, restrictions are minor, no drinking (zero tolerance), there are only as many people in the car as there are belts safety, there are no restrictions on when you can drive, etc. You can keep your Ontario license for when you return. You must pay a fee to change your out-of-province driver's license to an Ontario license.
The fee depends on the type of Ontario license you obtain. See a list of fees for changing an out-of-province license. The note on that website about receiving a 5 GDL license if you have had a Class 5 equivalent license for less than two years has to do with other provinces that do not have a graduated driver's license, or have a system that is less than equivalent to that of Alberta. The address on my driver's license belongs to my parents, although I don't currently live with them, because I was moving both as a college student and for summer jobs it would have been ridiculous to keep changing my address, so I can keep that address and still get all my mail and still be able to say it technically is my official residence, although I will sign a lease in Calgary.
To get the best car insurance rates, I had to provide an experience letter from my previous car insurance company and a standard driver summary from the Alberta government. I was looking at this page from the Alberta government about exchanging driver's licenses from another province, and it says you have to if you live in Alberta for more than 6 months. The documents I brought when applying were my car insurance policy, safety regulations certificate, current vehicle registration and driver's license. This means that the tickets that are attached to your Ontario driver's license will be known to the Alberta Ministry of Transportation and will appear on your Alberta driver's summary.
They also told me that I could take my G1 road test whenever I wanted because I already had my GDL Class 5 Alberta license for more than 2 years. You can get an Alberta Driver Summary in person at an Alberta registry, place an order outside of Alberta, or authorize someone to pick it up for you.