"I love you."
I think you're right. I just read a couple of explanations by Marek. He said ciebie is the stressed version of cię, and he remarked further that cię should therefore not be used at the end of sentences of more than 2 or 3 words. Ciebie should be used instead. I think it was he who also said on the other hand, you generally want to avoid starting a sentence with an accusative pronoun, unless you really mean to emphasize it.
It's possible, but it would need quite a specific context. Let's say someone says "I hate everyone!" and you ask "What, even me?" and they answer "No, I love you". Or in a way, "You - I love". That's basically how "Ciebie kocham" sounds - as if it was contrasted with other people.
Generally it's really rarely natural (or even 'correct') to start a sentence with a pronoun different than the subject pronoun.