I second what glennsfc said about no plywood. I would even be leary of using laminate. We used vinyl tiles on our floor (self-stick) 26 years ago. Then put an inexpensive area rug where the kids played (in front of the tv). That was so easy and bullet-proof with whatever the kids spilled. Arts, crafts, glue, it took so much abuse. Easy to change out the area rug every so often. When we laid the tile, we used a waterproofing film over the cement floor first before laying the tiles. Ours is a walkout basement. No water issues and I have only occasionally had to run a dehumidifier. (i.e. this summer only once) 26 yrs later the tiles are still down and I'm looking to replace them only because I'm tired of them but they are still stuck tight and will require some work to get them up. Tile is in the laundry room and bathroom down there also. We do have carpeting in a bedroom down there - just regular padding and carpeting. We have never had a mold or mildew issue. Never. You don't say if your HVAC system runs thru the basement? And do you ever need to use a dehumidifier down there?

IMHO - I would say that if you don't stablize the floor, then a hard surface product is out. Carpet would stretch as the floor moves. I have seen an orange underlayment that has a small block grid that is supposed to give and is used under tile (can't remember the name of this thing), but from what you said you have an up and down shift as well and I'm not sure this underlayment would work. Someone with experience with this may know better.

ditto w/the above posters Just went through all of that w/our basement - start outside first - especially helpful while downpouring - you may be surprised how the water is flowing off the roof/gutters - 1. landscaping pitched away fr. foundation 2. preferably no large plantings near foundation - they will attract water 3. gutters properly attached, pitched, draining away from home 4. you could try filling the cracks in the foundation to see how that holds up - 5.sump if necessary Waiting to see if your remedies work keeping moisture/water out before laying new flooring - in the interim get the carpet up/out and treat the floor -

Finished concrete (like epoxy) or porcelain. Nothing else is in the 'water proof' category. Rubber flooring will work (with a horrible smell and HORRENDOUS price tag) but it has been known to soak up mold if it gets wet. Sheet vinyl will work for the dumbbells. Your requirements will prevent you from looking at other products. You will need to pick a #1 requirement and then shop for that ONE requirement. You will choose the product that best fits all the other requirements. For instance, cork is great in basements but is not water proof. It is great for denting...but it will dimple. Etc. As you can see it fits many things but not all. Pick #1 concern and then find something that kinda/sorta/maybe fits your other issues.