Lots of good advice. As a late comer to this string, I can add little. But ... ditto on the 308 Win. Been using it hunting deer for 40+ years. Advice .... don't scrimp on optics. Bad move if you do. What is the best? My answer is the one you can afford. The competition is so keen that about any scope or bino in the same price range will be practically equal.
As far as a hunter safety course? Should you take one ... sure. In person will beat an online approach. But as far as gaining hunting skills ? I doubt that. The courses I have been involved in .. Alabama, Arkansas, Texas, New Mexico, Montana .... all were focused on safety, as they should have been.
I suspect with a military back ground you already are a good shooter, have been trained in map, camp skills, compass use , in decent physical condition, etc. That puts you ahead of the game. I would suggest that you get out in the woods a bunch. Scout where you plan to hunt. Look for "sign" .... such as game trails, last year's rubs and scrapes, food sources such as browse (vines, brush, etc.) and oak bearing trees.
As far as gear .... avoid the gimmicks. If it sounds too to be true, it ain't true. There are no such things as a sure-fire game call, or a bring-em-in from miles around scent, or the perfect cammo pattern. About any quality, quiet woodsy colored clothing will work fine. Though I go out now looking like a walking tree, Lord only knows how many deer I have killed while I was wearing denim bibs and a red/black plaid hunting coat I ahd bought at Sears.
Just like optics, don't go cheap on your hunting shoes/boots. You are going to cover a lot of ground, junky boots = blisters and aching feet.
Hope you have some good luck and welcome to this insane group of deer hunting enthusiasts.