According to William Morris :
My question is about securing the base 2x4 to the floor - or, if not that,
the bottom of my wall. I've seen nailers that use a .22 charge to drive a
nail into concrete, which sounds like fun. Since I don't have one of those
or any real long-term reason to buy one, are there any other ideas?

Yeah, they are fun, but they are a trifle dangerous ;-)

If you want cheap and you don't have that much to do, concrete nails
are the way to go. Wear eye and hearing protection and use a hand
sledgehammer, or even a full size sledgehammer. Reasonably quick
and dirt cheap, especially since the concrete floor isn't really
"concrete", it's a mortar mix, and much easier to pound nails into than
real poured concrete. But the bangs are _loud_ (just as loud as the .22
power drivers, if not more so).

Other approaches (eg: tapcons, drill&lag, Remington power drivers[*], hiltis
etc) are really more for larger/more difficult jobs (poured concrete, fast
installation, _lots_ of nails, higher strength requirements etc).

If you do go with a power driver, be _bloody_ careful and pay attention
at all times. When used properly, they do the job quickly and well.
But a moment's inattention or sloppy technique can put a ricochet thru
_you_ or someone on another floor or thru a wall. Make sure you match
the loads properly to the work you're doing.
[*] the afore-mentioned .22 power driver.
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.