What will this basement be used for? Hanging out? Storage? Is there a door down there or can people in the main living space see down there?

Laminate doesn't hold up well to water, and basements tend to be a place where moisture gathers. Something like LVP would hold up better. Usually faux wood and real wood don't work well together. So if the basement will be visible from the main floor I'd go for a stone look rather than wood. If there's a door or the area isn't super visible go for a contrasting LVP wood. Pick the lightest or darkest tone in the your hardwood and try to match that.

Thanks for your question. Since it is in the basement level, you should be able to use any floating type of engineered floors or Luxury vinyl. To keep it in the similar look and feel as your main level, it is not a bad idea to have this 7-1/2" Triangulo Brazilian Cherry floor floated or glued down on your slab.

Triangulo Brazilian Cherry Jatoba Engineered Floor Plank

Solid wood is never a good idea for the basement. I would go with a stone look LVT or carpet again.

It's all about the use of the space. If the basement is dark and dingy, then go with something that is super light (almost like a Scandinavian look). If it is a walk out basement with 9ft ceilings and a massive amount of light, then the depth of colour on the floor won't matter as much.

If this is going to become a public space (you will have guests over for movie night) then going with a higher quality product is part and parcel of the renovation. If this is a private space for the family to 'hang', then laminate will work very well.

Just make sure that you put the MONEY into the subfloor. Carpets hide the WORST possible substrates imaginable. That's why they are used. The builder can muck up the slab because s/he knows the carpet will hide the horrors of the bad pour.

A well prepared concrete slab (that used to be covered in carpet) can cost $2-$4/sf to 'fix'. That's normal. That is to be expected. Please budget for it. If you can get away with less, then great. But at least you will be prepared to pay the price at the beginning.

Once the slab is fixed, you can go ahead and put down any rigid floor you want. Engineered floating hardwood is not a problem. Laminate is not a problem. LVP is not a problem. Nothing is a problem so long as the concrete slab is fixed. But be aware that you will need to float the floor. We've got too many horror stories of 'glue down' floors in basements (or over old slabs) that were ruined (complete gut and redo) by moisture. Had those homeowners used a floating floor, they would not have had the troubles they experienced.