Music: beyond the most obvious picks (Frank, Dino, Tony Bennett), try mixing in some Coltrane, Nat King Cole (e.g., “Crazy Days of Summer”), Johnny Mathis, Nancy Sinatra, instrumental tracks from John Barry James Bond soundtracks (I recommend “On Her Majesty’s Secret Service” and “Diamonds Are Forever” for their grandeur and swank-itude, respectively), Dusty Springfield, perhaps a Noel Coward ditty or two, and at least one good compilation of “Space Age” music (contemporary alternative: Combustible Edison, which recreates that style pretty well). If you can find it, you could even mix in a bit from a 60’s comedy album… there’s a bawdy, blonde middle-aged female comedienne from that period who is now all but forgotten (and sure enough, I can’t remember her name now; her shtick was her very dated sex jokes and timely references to things like the Mercury Space Program) who would be a most interesting discovery for your party guests.
Food: check out James Lillek’s site (specifically, his “Gallery of Regrettable Food”) for period-specific recipies – many of which involve the use of Jello molds. There must be a few party finger foods there, though.
Needless to say, you will need a fully stocked bar, replete with accessories (cocktail shaker, strainer, etc.) and martini extras (stuffed olives, pearl onions, citrus fruits and peeler, Granny Smith apples, Angostura bitters, etc.) and a bartending book.
Good luck; it sounds like fun!