What rooms will the new flooring be installed in?

If you compare high quality LVP with high quality water-resistant laminate, they're about equal in terms of durability and performance. LVP can typically be installed in greater spans where most laminate can only go 30ft or so before needing a transition piece. Not all laminates are like that though, my laminate can go 66ft before a transition is needed. If you'll have it installed in a powder room you'll want to make sure you get water-resistant laminate and not the regular laminate (or go with LVP). I happened to like the look of the laminate I chose over the look of LVP and in my own personal tests it did not scratch as easily as LVP. We're SUPER happy with our laminate...I mop it with water with a damp mop, our two dogs chase each other and can't scratch it, and it's installed in our kitchen and bath. Ours is AC4 rated, 12mm thick plus a 2mm attached foam pad. For your home, I probably wouldn't even consider laminate unless it is water-resistant or you have tile at entries.

That isn't "black slab" concrete...that is cut-back adhesive and it should to be removed. Except it has to be tested for asbestos (those tiles really, really look like asbestos based tile) before you remove it. Cut-back adhesive had a long and glorious history of being asbestos filled.

Removal for adhesive is BEST done by grinding...except....you can't grind asbestos based adhesive (oh dear). Circular argument here we come.

Before putting down a new floor (especially vinyl) you will want to remove as much as 95% of that adhesive. But it might be filled with asbestos...so now what do you do? Floating a floor is a great idea...but it needs to be flat and even.

To do that, you need to grind off some areas and add concrete to others (which means the adhesive has to be ground down - except that isn't allowed with asbestos...sigh). Hair pulling starts looking like a really good idea at this point.

If your subfloor is flat *enough, you can throw down a vapour barrier (which you must have anyway) and then install a decent laminate. Vinyl HATES cut back adhesive. It hates it SOOOOO much (how much Cancork?), it hates it SOOOOO much that the black tar-like adhesive can STAIN the vinyl from underneath. And it can do it anytime from day one to day 500...but at some point, a floating vinyl plank is probably going to become stained (from underneath which will show through on the surface) in a rather short amount of time.

Laminate is more forgiving. Take the money a vinyl plank would have cost, and find the best laminate that money can buy....and get a nice, thick cork underlay to sit over top of that vapour barrier. It will offer a nice, solid floor underfoot.

But you have to check how level the floor is and then you have to test the adhesive (black substance layering over the concrete) before you try to do any form of leveling.

The flooring is going in my hallway, dining room, and family room. It's 440 sq/ft. Are you sure that this stuff can stain the floating floor. It's so old that the tile comes off whole with a putty knife and minimal effort. It literally took me 20 minutes to remove all of the tile from roughly half of the floor.

yep. same flooring and adhesive we found in our old house. Completely agree with Cancork above. Take his advice. It doesn't matter how easily it removes. That is not an indicator.

the black stuff is not concrete. It is adhesive. It is a contaminant. It is most likely FILLED with asbestos. It cannot remain if you need to do leveling.

The question you want to ask yourself is this: How much money am I willing to waste by ignoring the "staining" advice? This will stain vinyl that is laid directly over top. If you pay $4/sf for vinyl flooring and you need 500sf of it, then you could be wasting $2000 + installation effort/costs. Is that an amount of money/effort you are willing to throw away?

Good luck. As far as I'm concerned, there is PLENTY of work ahead of you...and you might need to pay for remediation. But you need to test the cutback adhesive to find out.

You have a toddler and another on the way. I would think the most important thing would be their health which means you need to stop pulling up what is probably asbestos tile and get the whole thing tested!

Stop fear mongering. First of all asbestos tile is the safest thing to remove. Especially when it literally is being taken out whole. Then there is the cut back. I asked a very simple question. I didn't ask for your moral judgement. If it will still ruin the floor I will gladly flood it with mineral spirits and remove it. Since it's a wet removal things will be fine. Then I'll lay down my barrier and lay the floor. The slab currently is level. Hopefully the cutback doesn't ruin that.

Did not notice this post before today.

Look into Ardex leveling and patching materials; many can be used over cutback adhesive to encapsulate and flatten concrete flooring.

Looks like asbestos??? Don't take a chance. Have it tested. I am being told by professionals that lots of flooring before 1987 had asbestos in it. I'm having mine abated!

No question that the floor in the picture contains asbestos. Floors like these that have lost bond to the substrate can be easily removed in situ. Any cutback adhesive resudue can be encapsulated with a proper Portland cement based flooring patch or underlayment. Some require a companion primer or an additive.