I think that the people who want to set the film in World War II are missing the biggest strength of Captain America, the "man out of time" thing. The kids who picked up Avengers #4 in the 60s would not have been familiar with the old WWII comics, and, while there are a lot of good stories told in the World War II-era in flashback (and in the old Invaders comics), Cap's real story is modern, not in the past. Irregardless, we should under no circumstances bank on there being more than one film, so he has to be brought into the present in the first one (by the same token, you can't leave that to an Avengers film, because that means that a huge amount of time must be committed solely to bringing Cap into the 21st century).
I would open with Cap and a couple of the Invaders on leave in the closing months of the war, briefly returning to the continental USA. They would be watching a propaganda newsreel, which would open the film, chronicling (40s style) the exploits of Cap and his team. Now, I don't know what Invaders you could get into the film, realistically; Namor is bound for his own production, and I'd rather skip Bucky (I don't think he'd translate well), so Human Torch (assuming there isn't some niggling issue with the Fantastic Four franchise) and Union Jack and Spitfire (they're not American, obviously, but along to see the "colonies"). Afterwards, they stroll along the shore. Then, they stumble across the Red Skull and his people; Germany is lost, but they're planning to destroy Washington with a doomsday weapon launched from within the United States. Big fight, etc., Cap launched on a rocket, frozen...
Cap wakes up from his dream in the 21st century; he now lives on the Helicarrier (if SHIELD is allowed in the film; Fury is also getting his own film, so maybe not); if SHIELD's not allowed, then some military base will do. In order to avoid too much time showing Cap's initial reaction to his arrival, I'd prefer to use a flashback structure anchored in the present, a few years after Cap's return. That way, you can show scenes of him being discovered, his initial reaction, as well as his origin in World War II, with a minimum of time. Sharon Carter, Agent of SHIELD/whatever agency substitutes for SHIELD, is Cap's chief partner in the field, and love interest (you could also have them already involved, just to subvert the usual order of things in superhero movies). Sam Wilson would be here too; whether as an agent or as the Falcon, I'm not sure.
The plot in the modern era revolves around a series of terrorist attacks that has Cap convinced that the Skull is still alive (he got away back in 1945), despite the seeming unlikelihood of that. Similar to what Brubaker did at the start of his run, use this conviction to trigger some judicious flashbacks establishing the Cap/Skull mutual hatred, and how their origins are somewhat meshed (he was created to counteract the Skull's symbolism). If we're allowed to use SHIELD, the Skull's plan involves commandeering the Helicarrier itself, and taking control of the global security systems that operate out of it. I'd also use some variation of Brubaker's current plot thread, where Cap goes to see a SHIELD psychologist to deal with his issues; except the shrink is Doctor Faustus, manipulating him to suit the Skull's plans. The Skull is alive thanks to various treatments devised by Dr. Zola.
The Skull should succeed in taking over the carrier, and use the weapons systems (nuclear, laser satellites, whatever) to destroy a suitably large city, killing millions; however, he's not a typical villain, out for millions of dollars in payoffs; he wants to institute a new world order, an demands that anyone who wants to avoid his wrath must prove their loyalty by exterminating various "undesirables" within their own borders, and, on a national level, nations of undesirables (ie, most of the non-Caucasian world).
Cap, Sharon, and Sam stop him, of course.
We should also find a way to work the "Cap windsurfs on a fighter jet" scene from Civil War #1 in, because that was awesome (perhaps SHIELD attempts to take down Faustus-brainwashed Cap; not only do you get the cool moment, but you neatly reverse Millar's intent, since SHIELD is actually on the right side of things).