The order shouldn't matter, unless you're on a hinged mast step, in which case it likely comes from the stern and up. In that case, you'll want the backstay attached just because, but loose. Not every mast can be raised and lowered with the shrouds attached, but if yours is one that can, you can do those too, loosely, to help with the side-to-side action a bit.
If yours is one that's crane'd into place, it won't matter what order you go in, they'll all line up as you tighten once it's in place.
I have an Oday 23 and used to lift the mast from the front. Like Geehaw, all the stays were attached but loose. Raising/lowering the mast is a two person job and I use a sheet connected to the triangle plate on the backstay to help with the lifting/lowering.
One word of caution ...... when raising the mast make sure that the turnbuckles are oriented correctly and are free to move in the right direction as the mast is raised and the shrouds begin to tighten - if they are not then it is easy to bend the screw in the turnbuckle. As we raise the mast we are watching each of the turnbuckles to make sure they are free and clear to move.
Once the mast is up and the backstay is attached I begin to tighten all the turnbuckles, first to take up the slack, then hand tight and then look at the mast and tighten to keep it straight and vertical all the way up.
I check everything after a shakedown sail when everything gets seated and stretched out. Here is a link to a good overview which covers all the bases about masts and rigging tuneups. http://www.thecoastalpassage.com/petrearigging.html
for a more detailed explanation I'd receommend this youtube video..... everything you ever wanted to know about rigging... https://www.youtube.com/watch?v=GuhVrb1gI04
Hope this helps.
It has been 7 years or so since we took the mast down on my 272...here is what I remember...the piviot hinge at the base of the mast directs the mast to fall toward the stern.....(fall is a bad word)....lower....we loosened all the side stays and told my wife to hang on to the forestay as we disconnected it at the stem head at the bow...we told my wife to hang on to the forestay and to 'not let go' and she did not....but she did leave the deck ....we had like two people holding the mast from on the cabin top and two in the back of the boat....it went very well but is a much heavier mast than I would have believed...do not tell your wife and children to hang on...as they may be airborne and your mast could easily be damaged....we did this at the slip...I think if I were doing again, we might do it at the crane....& .I need to do it again to find out why the masthead light works only infrequently.....a real pain ....good luck.....remember it pivots aft and you need some friends to help...I also think it's possible we disconnected the
lower shrouds and loosened the outer shrouds a lot....Good luck1
However, it works just as well by running the line from the a-frame back to a winch in the cockpit. I have done it. The a-frame works, but it provides little lateral support should the mast decide to slide to one side. I saw a kit to deal with this by tensioning the shrouds as the mast is lifted. You could also simply tie lines to the mast and run them through turning blocks abeam of the mast them back to jam cleats or clutches in the cockpit. You could mount those blocks on the stanchions(?). Using the a-frame scares the bejeebers out of my wife, so we normally have the yard hoist the mast. But admittedly, I had no lateral support for the mast.
Oh, and the mast step plate and the mast base plate on a 272 have a pin / slot configuration that will immediately break if the mast moves off center laterally. Total PITA.