Porcelain tile with a pei rating of 4 or 5 (commercial strength). Porcelain with pei 4 has a breaking strength of 400lbs per sq inch. Pei 5 is around 450lbs per sq inch.
Also look into epoxy or single component grouts. These grouts do not allow moisture to penetrate and are mold/mildew proof. You'll spend a little more for these products but you'll have an ever lasting floor, flood or shine.

I will recommend that you get a rubber mat for the barbell. The weight of product is not an issue but the force of it being slammed down very well could be. The rubber mat (at least 1/2" thick) would absorb most of the shock of the barbell.

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.