I always recommend tile first for any basement. If tile's too cold, next is carpet. If you ever have a severe moisture problem, carpet is easier to remove and replace than engineered, especially a glue down.:thumbsup:
Possibly another suggestion to add to your list would be an epoxy coating floor system. Cost effective as well as green products (ego friendly) available.
Make sure you take a ph test before you apply any epoxy or glue to the floor, if you don't it can be a waste of your time and money.
You can buy a kit at your local flooring company or concrete supplies. Check out raydonseal.com or duraamen.com, the test is done many differt ways, the easy way is by placement of calcium chloride test dish on the floor, wait approx 3 days, weight dish, then read chart. A test should be done prior to placement of ALL FLOORING on new or old concrete.
Thanks for the inputs. How do you test concrete for ph? That is something new to me.
I'm a big fan of luxury vinyl plank or tile, especially if moisture is an issue. Carpet is warmer and comfortable underfoot, shortest life, can get moldy and hold or breed allergens in a damp basement in a hurry.