There is a type of fastener designed just for this purpose, called a masonry anchor screw, or concrete screw. The ones I am most familiar with go by the brand name "Tapcon". There are quite a few varieties, but for use in your basement I would recommend the stainless steel. However, if your floors are pretty dry, the standard variety is coated against rust and should hold up pretty well. If you do not want to see the fasteners, you could counterbore the holes and plug them afterward.
I like the Tapcons because you can drill right through the wood and into the cement, then drive your fastener immediately. In fact, you almost have to do it that way to keep your holes aligned. Also, the holding power is really good - into regular concrete, a 1/4" Tapcon with 1-1/2" of embedment has almost 2000 pounds of pullout strength.
The length of the screw you need is found by adding the thickness of the material to be attached to the recommended minimum of 1" and a maximum of 1-3/4" embedment in the concrete. So, for a 2x4, 1-1/2" thick, a 3" screw would work well. A carbide bit of the correct size is supplied in the box. The hole must be drilled 1/4" deeper than the fastener will reach.
I like the Tapcons because you can drill right through the wood and into the cement, then drive your fastener immediately. In fact, you almost have to do it that way to keep your holes aligned. Also, the holding power is really good - into regular concrete, a 1/4" Tapcon with 1-1/2" of embedment has almost 2000 pounds of pullout strength.
The length of the screw you need is found by adding the thickness of the material to be attached to the recommended minimum of 1" and a maximum of 1-3/4" embedment in the concrete. So, for a 2x4, 1-1/2" thick, a 3" screw would work well. A carbide bit of the correct size is supplied in the box. The hole must be drilled 1/4" deeper than the fastener will reach.