I'm with the posters who feel that the first Cap movie should be WW2 based. Similar to what has already been said, I think Cap loses his relevance somewhat if he doesn't have a WW2 origin. Same with his main nemesis, the Red Skull.
I think the first film should be set in WW2. If it has a good script, cast, and direction it should work. WW2 projects are still being made, and some are still quite popular, such as Saving Private Ryan and Band of Brothers. Period pictures also run the gamut of popularity. I don't think the timeframe should be that much of a hindrance. Particularly because its some intimately tied to the origin of the character. Batman, Spider-Man, X-Men and Superman for example can be updated much more easily than Cap.
The first pic should be WW2. The second pic, and maybe third pics, should be modern day. I would also like a small mention or cameo of Isaiah Bradley in the first Cap pic. Of course it would be controversial for many, but I thought The Truth was an excellent work and I would like to see it acknowledged, albeit in a small way, in any Cap motion picture.