Personally all I want is to be some rugged motherf*cker crouching in the rubble with a shotty waiting for inexperienced wastelanders to come by to kill and rob.
The only thing of your idea might work is choosing either a trait or a previous affiliation from your backstory to side with, for example previously a member of a certain group in the game or a previously disbanded group that might have small remnants around. That way you might be able to have certain benefits from starting out, like as you said, military training with power armor, energy weapons. Or as a survivor, better survival skills and setting traps etc. I like the idea of joining groups if you wish but I don't want an NCR vs Legion thing all over again, unless there are some better choices and groups out there that all have a say in the matter.
But in the end all I want is to just start out with a set goal, usually the best is the skyrim/oblivion way of either being imprisoned or trying to escape somewhere which forces you to have no current items. Really all I am looking for is a perfect wasteland experience, I am not a big fan of the future tech aspect of the games. I would prefer to just be creeping around in tunnels avoiding ghouls clutching sporks and teddybears.
Skyrim did it pretty well and despite being dragonborn, you were kind of a bystander to an event that forces you then into situations, as opposed to NV where there is all this backstory and no choice in the matter and your backstory is just written for you.
One thing is for damn sure, I want to already be an adult and a f*cking bad ass one at that. That was the only major annoyance I had with the backstory and lingering story in Fallout 3, was being treated like a kid, despite looking like an awesome bad ass.
I definitely want people to react to me based off how f*cking bad ass I am, children need to f*cking flee as I walk into town.