I would get pricing from cruise line and internet. Then I would ask a qualified professiobal T.A. to book it, with an effort to match or come close on pricing. It is always best to have a T.A. working on your behalf.
Research on the internet then contact a reputable TA who should be able to meet the price and provide service like airline, pre-stay hotel, etc. The closest we have done was about 6 weeks out. We didn't think we could travel, but an opportunity came up and the price was right for a prime winter week on a brand new ship. TA got us some cabin perks from the cruise line too that we would never have received from an online agent.
Chuck has given you the best advice on this. Remember that the possibility of a lower cruise price may well be offset and then some by booking last minute air! Now for those of us who live close to a port sometimes we can get a great last minute deal from a TA that we have managed to gvet on their "A" list. My local agent once called me on a Monday and asked if I could go Sat for a 5 day at $250pp with the third just $59 and that included all port and taxes. (This was well before 9/11 and considered an unreal pricing BTW) Since then and in the last year we have on more than one occasion had less than a couple weeks notice with one time being booked on Wed, sailed on Fri
If you go thru the internet, be very certain it's a legit company.
Travel agent in my leads group had a cousin who insisted on booking on the web & when they got to Florida, their tickets were not valid. I can't remember if the cruise line made concessions & took them or not.
I buy airline tix & hotel reservations online all the time but only thru "big"companies.
And, yes you can do better at the last minute. I just booked a couple on the Dawn Princess (8/25 out of Vancouver) for $1299 each - outside with balcony & included$75 pp shipboard credit.