Get yourself a nice ramset.
I did basically the same thing...
I used pressure treated lumber on the floor. .
Then I used construction adhesive and glued the
2x4 to the floor. Once that was set where
I want it, I drilled a few small holes and
used the ramset to attach the wood
to the floor. I predrilled because the pressure
treated lumber is TOUGH stuff to ramset through.
Depending on the job, the ramset you hit with the
hammer is the cheapest. Only 20.00 or so.
The nicer one is a gun type that no hammer is
needed, just a little body weight. I went the cheap
route and it worked fine. I dont mind the smell of
gunpowered but make sure you DO wear some ear
protection and get the dog, cat, baby etc (if you have one)
out of the house. The sound of a .22 cal cartridge is fairly loud
expecially when its in a confined space such as a basement.