I tweaked your post slightly to improve the presentation of the image, the "/thumbs" part shows a thumbnail-image, by removing it you get the bigger picture.
Compressors:
The ones in the image are noisy little beasts without a tank. Living with the noise is up to you, since you have a basement I presume that irritated neighbours and family isn't an issue.
A tank eliminates the pulsations in the air pressure caused by the pumping action of piston type compressors. These pulsations will be a problem when trying to do fine detail works with the airbrush. Those simple compressors are good enough for learning the basics but after a while you will want to get one with a tank so don't waste money on an item you will replace after a while.
Since you have space (basement) I would strongly suggest taking a look at garage/mechanics/DIY/homeowner type compressors. The tanks on those are large enough to give you a lot of airbrushing time from one filling of the tank. Run the noisy compressor while you (and possible family) is doing something else. Shut it off completely beforeyou start painting and enjoy the silence, the low noise psssssshhhh from the airbrush can be quite calming but the RATATATATATATATATAT!!!!! from a noisy compressor (machine gun nest) rattles my nerves.
Make sure you buy a compressor with a pressure controlled shut-off, this will run the compressor motor until a pre-set air pressure is reached, when you consume air the pressure goes down and the racket starts again. My reason for telling you to shut it off completely with the manual power switch (or pulling the cable) is that the air pressure limits for these automatic shut-offs are usually set at 6 psi (on) and 8 psi (off), since you will be spraying at 2.5 psi or lower there will be lots of usable air in that tank when the RATATATAT starts at 6 psi. This can be quite startling when you are fully concentrated on your work.
By cutting the power to the compressor you can enjoy all that air from 6 psi down to 2.5 or 2 psi before the airbrush starts losing its mojo.
A compressor with a 2 gallon tank is plenty big enough for airbrushing, if you want to run air powered tools (nike guns, grinders, et.c. and so forth) you need something bigger.
If space/noise was an issue I would strongly recommend getting a silent compressor (as noisy as your fridge).
These cost a lot more, US $400 and upwards ....
Building a sound isolating enclosure is cheaper, being in an other room is the cheapest way.