Normally I plant lemon or sweet basil. The store didn't have any, so
this year I planted some other variety. A bunch of plants popped up,
but their leaves look a bit like oak leaves, with jagged edges, and
some have already started flowering here in NY even though it's only
June.

Is this basil? Or did some weed sneak in? It's new dirt from the
store, but anything's possible.

Also, if anybody knows a website with pictures of different basil
leaves, that would help.

Thanks!

I Don't know but there are several different types of basil. You could maybe do a basil search of the web and find pictures of the different types.