No under layer on mine, has been down for several years now and works great. We liked it so much we put some in our bedroom. Over the concrete slab it does not work as well. Under furniture it will edge-lift, very annoying. I guess at some point I'll have to tear it out of there. There are other user reports on issues going over concrete, especially in basements.
The floor is designed to float over the subfloor, so you don't want heavy furniture on it or seal the edges so it can't move - expand and contract with temperature variations, much like a click-lock laminate flooring. This keeps it laying flat.
Like I say, great in the RV but not so much in the S&B.
I can't comment any various types, I used the Allure from home depot, they are the retailer for it, has a glue strip on 2 sides, they stick together. Since it's done in pieces, or planks, the cutting and fitting installation is quite easy. What is surprising is the adhesive is so strong you'll ruin the tile trying to separate them once stuck - but it will un-glue itself under furniture when applied over concrete. Very odd.