You don't need to get an FMM before booking tickets. If you're flying, you don't need to visit that web site at all.
The current procedure is that you will be given the FMM form during the flight to fill out before landing in Mexico. You will pay the fee to the airline as part of your ticket price (IATA code UK on your ticket receipt). You show the FMM at immigration when you enter Mexico, then keep it and turn it in when you check in for your flight departing Mexico.
You can also purchase the FMM in advance from the gob.mx web site, as you have discovered. In this case you will have already paid for it. The web site will give you the FMM that you must print, show to immigration, and turn in when you leave Mexico. If you're flying you shouldn't do this, since you have already paid the FMM fee via the airline. Buying the FMM in advance is advisable when you enter Mexico by road, as you may find it difficult to get it at some border crossings.
(Mexican citizens and residents are not supposed to be charged the FMM fee (IATA code UK) or the departure tax (IATA code XD). If you are a Mexican citizen or resident and were charged this, your airline can issue a refund.)