Generally speaking, if you are below or at grade which all basements are by definition I would recommend tile. I would also recommend an isolation membrane such as the one offered by Schluter. It will go along way in preventing cracks in the future.

Cork is a great option in basements. You will need to work with the floating floor (click-together) version. In basements you will need a vapour barrier (6mil polyethylene sheeting = $0.06/sf at HD) underneath cork or laminate. Cork works well as a thermal and acoustic insulator...something tile cannot do (tile is very cold and very loud). Laminate is normally quite cold...bot nothing compared to tile. Acoustically, laminate can cause a space to become louder ... but it can be taken care of with high-end underlay.

In Canada, the favourite place to install cork floating flooring is in a basement. I've sold 10,000's of square feet Canadians who's basements are freezing. Many of them state that they can't hear the teenagers hanging out in their basement because the cork reduces the sound transfer UPWARDS. Yes. TV's and voices travel upwards. Because cork "eats" sound, there is less noise to travel upwards into the living space. For play spaces this noise reduction can be a bonus.

Laminate and tile can be used...they are cold (especially tile) and to counter the "cold and loud" of the laminate you normally have to purchase an underlay that is almost as expensive as the flooring.