I don't have time to read through all the different ideas presented and respond to them. I just want to say I think having the first movie done entirely in the WWII period would be a mistake. I don't mean that the first movie would be bad; you can make a very fine period film, but its future films, whether is Cap 2 or the Avengers, they will suffer from it. Here are my reasons:
First of you will have this huge style change between the two. With all the time between the movies it would just feel really weird. I know a lot of people don't focus on the style, the aesthetic looks, the set universe created, etc. But if you separate these two periods it will feel like two different types of Cap and ultimately the first one will feel like an out of continuity movie. Having both periods in one movie will maintain the look, the feel and the casting during the transition.
Second, I feel there are two major interesting aspect of Cap. One is his time displacement, and the other is his legacy as a super soldier. I feel that the time periods are better from a general view, but also needs more time to be really interesting and to be done well. I don't want the Avengers movie to be cap waking up having a few scene of "Woe is me" and then jump right into action. I think Fury would let Cap retire, not force him into a fight. And I think it's really important to get this character development right. To see things as he sees them, to go through this journey with him, to see him compelled to take up the shield again and find his place in this new world as it's protector. This "man lost in the modern world" story will be lost and we will lose the most interesting aspect of the character.
My third and final reason is that the Avengers movie will already have a tin of A–list actors and the potential for great interactions, but they will have to cater to Cap and his story. The Avengers movie should be about the team, maybe two characters have more focus, but they should dominate the screen. I don't want all these great characters to become glorified cameos. It should be cap, the unsure leader, Tony, they party boy who's more of a loner, Thor, who's against the very idea of a government super team, and Pym, the jerk. I feel these interactions would work much better if the film didn't have to go into Cap's revival.
So here's my basic idea for a Cap movie. Act 1 takes place entirely in WWII; we get two big actions scenes, background on his origin and home life. Act 2 is his unfreezing and journey to understanding the modern world and finding where he belongs, Act 3 He is compelled to take up the shield and fight finding and accepting his place in the world. Last scene is Fury talking to him about the avengers. I have a more detailed idea but don't feel like typing it out.