Isn't there something about having to choose any Independent Character; and if you don't have any of those, instead any Character? Don't have access to by books just now, but so that you can't have a Tactical Squad's Veteran Sergeant as a Warlord before your Librarian, or something. I'm forgetting the specifics of it, but it still doesn't affect the difference between a LoW or an HQ, so it's not too relevant to the OP's question (which has already been answered handily)