Which choice is correctly punctuated? I know exactly where to start my research: the library. The library is a great place: I like to research. I choose to do my research; at the library. I started my research; at the library.

I don't see why you would need a colon or semi-colon in the last two sentences, so they're not correct.

The first two are more tricky, but one of the uses of colon is an explanation. I think this is the case in the first sentence (that's my final answer) and the second sentence would be better with a semicolon.