OK...so the hardwood is staying and the rest is being removed. Ok. No problem. There is probably going to be a floor height issue (assuming all of the old floors touch one another on the same level). That's OK. You can throw down an uneven T-molding where the hardwood hits the carpet/vinyl. Or you can raise the lower levels up to the level of the old hardwood. No problem.

Now...onto LVP OVER TOP of hardwood. Not a good idea. But it is what you want. So here is what you will need to do: sand down the old hardwood so you are on 'raw wood'. You will then treat this as a wooden subfloor. Great. Perfect. If the hardwood can be saved at a later date (ie. it still has plenty of wood left on it), then you will want to put down some sort of craft paper (cannot be a vapour barrier).

LVP and hardwoods don't like each other. Hardwood FINISHES (the stuff you have to sand off) have a chemical reaction to vinyl. Each contain active chemicals (even when dry) that can and will discolour the other one. The hardwood finish will stain because they are touching vinyl planks (usually a nasty nicotine orange). And (more importantly for your new vinyl) the wood FINISH will stain the vinyl (the chemicals leach UP into the vinyl and then discolour the new vinyl).

That's not all. The vinyl can and will 'cap' the hardwood. This prevents the hardwood from breathing off the moisture in it (or in the basement...etc) like it has been used to. The vinyl prevents the moisture from evaporating off. That leaves the moisture to hit the back of the vinyl and drip back down onto the hardwood. The drips turn to puddles once the wood has been completely saturated.

It can be one H3LL of a mess. It won't happen in the first year (if it does you have a bunch more issues) not even the second year. But it will happen. And then you HAVE TO PULL the hardwood...and the vinyl. And maybe even the subfloor.

So ripping out the hardwood sounds horrible but it is the best plan. To be clear, vinyl needs SUPER FLAT subfloors (hardwoods are rarely flat). The better option would be laminate. Laminate gets along very well with hardwood. They are both made out of the same stuff. And both breathe (a snick) which means they rarely have issues with one another.

Very helpful but click or glue which is preferred?

We had LVP installed in our basement after a frozen pipe separated and ruined the carpet. We went with click together even though it was a bit more expensive. This was based on two main items.

1) With the click together you don't have to worry about adhesive failure and edges starting to separate, and:

2) The LVP is 100% waterproof so if we ever did need to remove it because of water it could be reinstalled.

Over in-tact hardwood, the 'option' (which is a horrible idea....but everyone needs to learn at their own pace) is click-together. The glue will most certainly ruin any form of flooring it is sitting on.