The first thing I do is look at my budged, how much I want to spend
. I usually wouldn't hold back on the speaker and the amp, because this is essentially what gives you your quality and (SPL) sound pressure level. To me a sub woofer is important because not all the speakers can play those low frequencies, and for you to hear those frequencies you need a sub woofer dedicated to play those bass frequencies. It is also important to get the level of the low frequencies right, what you want to reach is an audio system that have a flat frequencies responds.
The sub woofer speaker is a speaker that must be able to move large amounts of air particles, this means the sub woofer must move large amounts. The low frequencies speaker is a power hungry speaker, the sub woofer have to be able to work hard. Low frequencies have big sound waves.
When you look a sub woofer don't buy the cardboard diagrams, go for the plastic types of diagrams. The sub woofer have a slew rate, this is the amount of time it takes the sub woofer to go from maximum positive or negative to go back to zero or rest. I would prefer you buy a amp with a slew rate of 1000 to 5000.
Next you need an enclosure; the enclosure prevents phase cancellation between the front and the back of the speaker. The bigger you make the box the lower frequencies you will prevent from phase cancellation. The port works like a flute, except it plays low frequencies. The best advice on the enclosure I can give you is to go and have a look at the spec sheet of the speaker.