Well, when I rode Western at beginning levels, we NEVER posted. Only sat. Warmup at a walk, then sitting trot.
I ride English now, and we will sit the trot usually after some walking and a little posting. However, I do sometimes ride bareback and while I *can* post bareback, it's not pretty, so we usually just go with sitting trot. So, it would be walking and then sitting trot.
I have never waited to sit the trot until after cantering. However, it may be that different horses have different needs. For instance, my horses now are on pasture 24/7, and supposedly because of that they don't need a lot of warmup before engaging in more strenuous riding.
"Saddle fit -- it's a no brainer!"" - random person