As with any professional correspondence, you don't want to seem too stiff or formal, like you're writing a letter from a Victorian template or a bad spam email asking someone to send money to a deposed prince overseas—but you also don't want to be too conversational. You're not in a dialogue yet, so it's important to treat this like a professional first interaction, and not like you're skipping several steps and asking to meet for coffee. The tone you're reaching for is, "You don't know me yet, but I'm interested in your company and want to tell you more about why."
Go with one of the classics, because they're used for a reason. If you sound too stiff and formal, it comes off like a holiday card. If you reiterate your call to action, it can carry a whiff of desperation. Just get out gracefully and quickly once you've said your piece.