The moisture issue is your real problem here, not the flooring itself. Even though LVP is waterproof, concrete wicks moisture from below, and that moisture trapped under your planks will cause them to cup or separate at the seams. You absolutely need a vapor barrier before anything else goes down. Most people use either a thick polyethylene sheet (6 mil minimum, really 10 mil is safer) or a dedicated moisture barrier product made for this exact situation. Tape all the seams and run it up the walls a few inches so you're creating a real moisture break between concrete and flooring. This step is non-negotiable if you're getting spring dampness.
Once that's sealed, click-together planks are honestly the way to go for a basement. They're faster to install, easier to replace individual planks if something goes wrong, and they let the floor float slightly, which is better when moisture content changes with seasons. Adhesive-backed planks are typically used when you want maximum waterproofing in the seams, but with a good vapor barrier underneath, click-together gives you flexibility without much downside. Add an underlayment on top of your vapor barrier - something with a moisture barrier built in. This cushions the floor, deadens sound, and adds another layer of protection.
The whole sandwich should be: concrete, sealed joints, vapor barrier taped at edges, underlayment (moisture-rated), then your LVP. Take your time with that vapor barrier because shortcuts there lead to ruined flooring in a couple years. I've seen basements where someone skipped it thinking LVP alone would handle moisture, and they regretted it. Do it right once and you won't have to rip it all out later.