I change my oil and rotate my tires at the same time. Used to be every 5000mi., But my new truck wants it done at 3500. I'm too lazy for this, but the ft. tires start to set, so it has to be done. Thus, at 4K the tires get rotated and the oil gets changed. Too soon for the oil, I know. I'm thinking of letting the tire dealer do a rotation at 3500 and then I'll do another at 3500 and change the oil. Synthetic. Should work out just fine. I'll just have to keep an eye on the dealer. Haven't found one yet that does a proper rotation. Last time I caught the fool crossing to the left and bringing them straight across to the right. Made him do it over. Gotta watch 'em.
As to the proper sequence, there's only two ways, as far as I'm concerned. Forget what the owner's manual tells you.
Rear wheel drive: Cross the fronts to the rear and bring the rears straight up.
Front wheel drive: Cross the rears to the front and bring the fronts straight back.
I do a 5 tire rotation, but I'm one of the few, so I won't go into it here, unless someone really wants to know.
Every time I rotate it feels like I'm riding on new rubber, for the next 500mi., even when the tires are almost gone.
The two main reasons for rotation are: 1)even wear for the life of the tire.
2) prevents radial tire pull, noticeable mostly on ft. wh. dr.