The process is the same. You don't need a fancy chamber gauge unless you believe you chamber is out of whack, or are loading for precision.
If you gun can safely fire factory ammo, then it can safely fire a spec Fl sized 308 reload.
Yes you can use winchester brass but I don't recommend it. I prefer R-P.
I recommend the lyman headspace gauge (not the same as the mentioned chamber gauge) for checking your completed ammo to make sure it will smoothly chamber.
The only real extra process for the M14 you have to watch out for, is primers and priming.
You have to make sure the primer is seated properly. I recommend getting a lyman primer pocket uniforming tool. It'll cut the primer pockets a touch deeper to make sure your primers seat below flush. And then I recommend using a RAM Primer, not the one on press, or the hand tool. It will help make sure you primer is seating firmly as deep as it will go. Once that's done, you have to make sure you don't use too soft a primer. I ONLY use CCI 200 primers in my Norc M14, and have never had a problem.
Keep you eye out for head separation and or toss your brass after 3-4 firings, and enjoy.