Which should I say:
I'm looking forward to our meeting.
or
I look forward to our meeting.
These are both correct. I would add, though, that I'm looking forward to our meeting sounds (to me, at least) more conversational (and a bit more genuine), whereas I look forward to our meeting is a bit more formal/polite. I would expect to find the I'm looking form in spoken language, and the I look form in writing (likely at the end of an email confirming a meeting).
I'd say that it's six of one and half a dozen of the other. But I always use "I look forward to...". Just my personal preference: it's shorter.
I am looking forward to our meeting with verification with email. All email and invoices need to be direct verification an right business formatting instead of not useful data information on them.