I've done a fair bit of reno work and know some of the local building codes (Quebec, Canada).
Generally speaking, treated lumber should not be used within living spaces. OK, that hasn't stopped me from using it as a sill plate for an exterior door but you should be aware that treated wood is not intended for interior use.
Wood should never be installed directly onto concrete. Most concrete surfaces within a home have a dry, interior face and a wet, exterior face (i.e. basement floors and walls). Concrete is porous and, given the right conditions, will wick moisture. The modern construction technique is to isolate wood from concrete using a moisture-resistant barrier that also serves as a thermal break. Go to your local building supplier and look for a roll of (pink) closed-cell foam about 4" wide. Place the foam strip directly onto the concrete and then place the 2x4 onto the foam.
Concrete screws are your best bet. Buy a kit that includes screws and a bit. You don't need a hammer-drill but it will make life easier. Tapcon screws come with a Robertson head (the "square-hole", popular in Canada but not in the US) or a hex-head. I like the hex-head variety because I can apply a lot of torque with a cordless drill and hex-socket. If you use concrete screws, make sure you drill a clean, deep hole. If the hole is shallow the screw will bottom out and you won't be able to drive it in fully. If the hole is filled with dust and debris, it will present too much resistance and you will break the screw while driving it in. A nail gun, the kind that uses 22 caliber shells to fire nails into concrete, is loud, dangerous, and can spall the concrete (i.e. break off flakes of concrete). I used one in the past and now prefer to use concrete screws.