I think we will level up pretty fast at first.
Plus I bet we start the game with a couple of perks to represent our past experiences.
If nothing else, if you are level 1 then you should have at least 1 perk.
And we always had 3 tag skills in Fallout so I'm betting that we get 3 perks to chose at the start of the game.
I heard that in one of the demos, the Sole Survivor was level 2, but had a total of 31 points of Special stats but I'm not able to cite it.
As to Strength Requirements on weapons, I'm betting perks have replaced that too.
So if you have a high enough Strength you can get perks to help with the recoil of your sub machine gun or if you have a high enough Perception you can get perks that increase your zoom or allow you to hold your breath when you fire your sniper rifle.
So if you are a wimp, you can still fire an M60 if you are careful bracing it and use bursts of fire.
But if you want to Rambo it, you need arms like Rambo so you have Strength enough to get the perks that help offset the recoil.
So rather than give you the stick if you are too weak for a weapon, they give you a carrot if you are strong enough and get the perks.
I like how perks represent training and experience allowing you to do better than someone without the experience or basic ability (high enough stat).