I know I'm late to the party, as I only just now saw this thread, but here's my two cents.....
Randen and others - Light Tubes (fancy modern tubular skylights, which I am generally a fan of) are not likely to be useful in this situation. In December in southeastern Wisconsin, sunset is at 4:15 PM, and (No joke!) I haven't seen the sun in four days. As much as I love skylights and solar tubes, I know they wouldn't work in my garage, and Daox is in the same part of the country.
In Doax's original drawing, I like simply having two 4 foot fluorescent fixtures on either side of the left car bay. It's a good amount of light in the right location.
I'm a big fan of ELECTRONIC ballast fluorescent's. Menards has American Fluorescent brand 4-foot shop light fixtures for $17.98 each. They are pre-wired with a standard wall plug, have electronic ballasts, and will run T-12 or T-8. Those fixtures with T-8 daylight tubes in them are GREAT! They are well made, good quality fixtures at a very affordable price. Best shop light out there.
They are MUCH better than the old magnetic ballast fixtures. ZERO flicker, more energy efficient, and much faster warm-up time when cold. (Important for an unheated garage.)
You can use those funny little adapters that let you convert a bulb socket to an electric outlet. Then plug the fluorescent into that. You then just keep using the same light switch you always have. You can also get an adapter that is a T off the original bulb socket. That can give you a power outlet AND still have a bulb.
In the four existing bulb sockets, put in LED bulbs. (Tim, how many of the Feit bulbs did you get?) You can get LED bulbs now for $6-$7 dollars each.
Here is my current favorite LED bulb -
TCP multipack at Home Depot
Even if the fluorescents take a moment to warm up, the LED bulbs come on instantly, so you have plenty of light right away, and even more when the tubes come to full brightness.
The LED tubes are nice too, and are good long-term investments. Still a little pricey at the moment if you want to buy a bunch. If you do want to use those, as others have said, just use old (cheap) fluorescent fixtures to modify.
Just my two cents...
PS: Robaroni - Too true about smashing fluorescents. I broke a 100 watt CFL once. (Not 100 watt equivalent... 100 watts, which is a HUGE CFL!) Big mess. Another advantage of LED is shatter resistance. The bulb-style LEDs are great for trouble lights, clamp-on lights, and "painters'" lights. Those are ones that tend to get moved around and knocked over a lot. Incandescents get hot and the filament gets shaken to death, CFLs have a warm up time and are a mess when they break, but LED bulbs in those fixtures are GREAT!
PPS: Another great place for an LED bulb is in the light socket of an automatic garage door opener. Openers shake a lot while moving the door (which is bad for incandescents.) The warm up time on a CFL in there isn't ideal when you just want to quickly put your can in the garage at night. Also, I'm amazed at how the shape of a CFL picks up dust. No joke, please regularly check any CFLs in a shop or garage. It cuts down on your light AND is a fire hazard. An LED bulb in the garage door opener comes on instantly, at full brightness, doesn't get dusty in the same way as a spiral CFL, and is energy efficient.
PPPS: Tim, those 19w LEDs that you got, did you mean that those were LED tubes for the fluorescent fixtures or standard screw base for the regular bulb sockets?