Take a look at the specs on the sub - there's four important numbers on there, and one less important one that's usually the biggest.
The first one is Qts, or System Q. To cut a long story short, for free air mounting you want a Qts between 0.65 and 0.9. Lower and you'll get very little bass, higher and you'll get a one note boom with very little bass below that. Ideal is 0.7ish.
The second is Fs, or Resonant Frequency. Essentially, in a free air setup, this is the lowest note the sub can play, without resorting to equalisation. Considering that a properly set up sub should only handle the range up to, say, 100hz, you want Fs to be fairly low. No need to get all the way down to 20hz, though, there's very little musical content down there, and you won't be able to tell over the road noise anyway. So something around, say, 30-35hz is sufficient. No higher than about 41hz (the low E string on a bass), though, or you'll lose musical content.
Which brings us to size. Some way bigger is better, others say that big drivers sound "slow". I tend to find that big drivers have too many compromises in their design to sound terribly musical. I don't like 18", and I've never seen a car audio 15" that I liked, although there are pro-sound drivers that size that sound OK. 12", or, better, twin 12" is a good compromise. Bigger drivers tend to have lower resonant frequencies, but don't buy them just for that.
Next, consider X-max, which is the distance the driver is designed to "throw" the cone without damaging anything. What it needs to be depends on how loud you need it to go, but basically, I wouldn't bother with anything less than 10mm.
And finally, power handling. On a lot of cheap subs, this number is basically a lie. Back in reality, realise that, if everything else is done right, you'll get about 86dB from just 1 Watt, 96dB from 10 watts, 106dB from 100 watts, 109dB from 200 watts, and 112dB from 400 watts, 115dB from 800 watts, and 116dB from 1000 watts. Or, to put it another way, get one rated for around 200 watts RMS, and ignore the pure fiction "Peak" figures.