Re: Vinyl/linoleum underlayment
3/8 underlayment is fine under vinyl. I've seen the other products you've mentioned used, mostly because the installer is able to purchase them at his wholesale flooring house. If he had to purchase that material at a big box or lumber retailer, it would be too expensive to warrant its use.
It is your preference whether you use deck screws or ring shank nails to do the job. I've used both. IMHO, screws hold better, however they're a little more tedious to install. Ring shanks are cheap and easy to install, and if one is a little proud, all it takes is another smack of the hammer to set it.
Don't forget to use a floor leveling compound to fill gaps and divots from the fasteners, otherwise any imperfection in the underlayment will telegraph through the vinyl and look terrible.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!