What is the best method to install new vinyl flooring?

If its only 1 layer down, most manufactures ok it it to go over the existing as long as its in decent shape like you say. Yes the use of a luan or birch luan is the best way to go. The new glue will take to the pores of the wood the best.Filling in the seams w/ a special cement based filler and if theres any imperfections in the wood. I ve always have used Ardex but there are other names out there.

Any questions you can e mail me through my avatar. GL

You may be able to install new flooring over your old. Check with the manufacturer of you new flooring to make sure that it is approved for it. A professional would probably put down a 1/4 underlayment (not necessarily luan) as some flooring requires birch. Stay Safe

I put vinyl planks on top of my old sheet vinyl which was in excellent shape but ugly. Since the vinyl planks float and aren't glued down, I was able to use a product called embossing leveller, which filled in the textured bits(you know, those annoying little dips that dirt gets caught in) of the original floor so the texture didn't show through to the new vinyl. I don't know if you can use embossing leveller with sheet vinyl that needs to be glued down.

get the job done professionally it will definitely be well worth the extra expense