what should I wear under a black v neck sweater?

black collared shirt

Two different tones of black = likely to mismatch = likely not to look good.
Black sweater + olive green = cold colour + warm colour = not likely to look good.

Best would be imho a chocolate brown sweater with the olive green shirt... or a beige v-neck. I think that black clothing in general rarely looks good since it doesn't harmonize with most complexions.
But since the sweater is not to be discussed I'd say go with the white tee.

White button-up shirt. Freshly ironed, and the crisper the better.

Olive green under black? That can't possibly turn out well. Go with the white shirt. Then go buy some non-black sweaters so you don't have this problem later.

Of your two options, I would pick the dress shirt. I like the button down and/or shirt/tie under sweater look, myself.

Oops, I thought the white shirt was a shirt shirt, not a T-shirt. Huh. Then I don't like either of your options.

I'm amazed that people think that black clashes with olive green. It doesn't.

I didnt think it did either, but there are plenty of rules of style that I dont know. Or follow.

I dislike white t's under dark sweaters and I have no idea why you'd wear olive green.

Get a dark navy tshirt or a bright color that pops.

I agree. I don't think t-shirt under a V-neck sweater would look right no matter what colour you're weating. You could also go with a nice light blue.

I like this idea. Just make sure the t-shirt isn't a 3 year-old rag from the Gap that has been washed 100 times. Or one of those 3-pack cheapos. Those are only good when you don't see them.

Also olive green could work, depending on your skin tone, and if there was a pattern in it.