If it was me I would use a white cake...when I add flavors I add them in place of the water in the recipe. I still add the oil but replace the water with my new liquid of choice It may be fine with a yellow cake as well but I like that...
If you need something geared towards that age maybe a gift box cake ( confetti cake ) maybe in those colors as well. Is it for a Man or Lady?I was guessing Lady .
Why not turn the cake into a "Birthday party" It self.Maybe have records on it one that's tittled 'Happy Birthday" and different candies ( look up what was popular then) party hats... Maybe add an old style banner with the Persons name...
I agree from what you can tell by the photo you posted It looks like maybe it's a 45 record sleeve?So something to do with music or records or maybe even those gumdrops that are scattered around?