The 0720 flight (flight number ZB 1376) to Venice Marco Polo is with Monarch.
The Monarch check-in desks open at 0420 for that flight and close at 0640. However you're also required to be at the departure gate by 0640, so checking-in earlier than 0640 would actually seem to be required (in theory at least):
http://www.monarch.co.uk/faq/flights/check-in-and-identification/check-in
(In practice though, departure gates often aren't even open at their official closure time. I've arrived at departure gates only 10 minutes before a flight on several occasions and never had a problem boarding).
I usually target my arrival at an airport between one and one and a half hours before the flight is due to leave but I've always checked-in online and never have baggage to go into the hold. Around two hours would probably be better for someone who is unfamiliar with the airport, not checked-in online and with hold baggage. (Like others above, I'd regard the suggestion of 3 hours as ridiculous!).
So, in your situation, I'd be looking to arrive no later than 0530, allowing just under 2 hours.