We technically booked our photographer first, though our venue was also holding our date for us until we were able to pay the deposit and sign the contract. It was around a month in between when we signed the contract with our photographer and when we signed the contract with our venue.
I'd say it's a toss up between venue and photographer. If you want your engagement pics taken early, I would go with photographer and let them know the few dates you have in mind for your wedding. Most of the time, they'll take those engagement photos, and by the time they deliver them to you, your date and venue are locked in!
Officiant. It was super important to us that our rabbi could officiate our wedding, so we consulted with her first to see which weekends she was available during the month of June. We then booked our venue the next day.