With the floor already painted, tile is out unless you sand the paint off. And I wouldn't choose either paint or laminate. Laminate is noisy. Even good laminate with a good underlayment. And it's not cheap.

I'd do a floating LVT floor like the Allure from Home Depot. There are a LOT of brands out there, not just the Allure, but you want one that either snaps together or has the overlapping glue strips like the Allure. If the floor is painted, that's a vapor barrier right there to help with the water transmission issue. Not that hydrostatic pressure can't lift the paint off, but unless you have a lot of moisture with a lot of pressure, it will be just fine.

Thanks LWO! Do you recommend the vinyl tile or the resilient vinyl plank?

Here is a link that might be useful: Allure Vinyl

If I love the cork after its installed in the kitchen, our basement is getting floating cork flooring! I noticed it was in the most recent Family Handyman basement finishing feature as one of their choices, so I must be headed in the right direction. They also mentioned possibly putting a dimple mat underneath, I haven't gotten that far yet to see if that's something I want/need, I just got my kitchen walks back this week! I'm only allowed one disaster at a time :-)

Thought I'd weigh in on this because my parents just had the same dilemma and went with ModuTile - it's an American made product that snaps together. And apparently if you ever have any moisture problems, you just pop them up, dry out, then snap back down. I included a pic from my parent's basement. Hope that helps give you some more options!

ModuTile is a good option. I'm still in decision hell myself. I put down eco rubber backed carpet tiles. Good quality but a year later i had a small flood. So they all went out on the lawn to dry, it rained, ...lol. Back down and another small flood. (just the back 1/5th of the floor) but still enough to be a pain. My moisture issues are almost solved in that area but i still have some research to do. An exterior corner that is a few feet below grade needs to be excavated and dealt with properly from the outside. New hot water system and washer hoses solved the earlier issues.
Still, a snap system floor meant for basements is the way to go. Getting a good bond to the existing slab might be a loosing battle. When i pulled up the original owners int/ext wall to wall,
The grid lines and glue are visible from the original vinyl tile that obviously failed.
I've considered the rubber snap together for the back half where we have storage and workroom. I don't want anything that would absorb moisture.

Here is a link that might be useful: rubber tiles

What about Congoleum's Airstep vinyl sheeting? I am considering using that throughout my dry lower level (split foyer home).

I have carpet in the tv area and wood laminate in the "play area". Very happy with both.

Another choice is an attractive vinyl sheet flooring.

No way would I want tile -- too cold and hard.