Shopping tips:
Head-unit
Get something with the following:
Must have BT (optional)
Must have rear USB (optional)
Must have 3 sets of pre-outs one dedicated to sub.
Amplifier
Get something with the following:
Crossover you can turn off
High damping factor >300 for multichannel amplifiers
For Sub amplifier look at the voltage that it shows for the RMS given- you want the rms given at 12V-13.8V
Get a 4ga amp kit, save you headaches later if you want to upgrade.
Speakers
If running amplified you want to match impedance with your amplifier (+/-) 10% you can go +100-200% if you are running active (controlling the frequency each speaker will see from the head-unit, and each speaker is on a different channel of the amplifier).
If not running them amplified then look for a high sensitivity (efficiency) 91dB+
Subwoofer
500wrms or less will do fine and will not require battery/alt upgrades
As far as size a single or pair of 8's, 10's, or 12's will work fine. The key to Subwoofer selection is amplifier it is matched to and the enclosure you put it in (designed to specs always sound/perform better).
Battery/Alt
Always a good thing to upgrade remember that the alternator makes the power and any additional batteries added to the system will add more stress on the alt.
* Amps and Headunit will usually take up most of the budget! So you want to optimize those first. Remember Speakers/Subs that take alot of power are cheap, the amps to power them are not, roughly $0.75 to $3 per watt produced.
All brands are not created equal when it comes to performance.
I would suggest you stay away from JL Audio amplifiers unless you are prepared to pay for extra batteries or even an upgrade alternator, these amplifiers pull a lot of amperage and have wrecked havoc on many a systems due to lack of electrical.
Brand recommendations
Speakers/ Subwoofers:
Bravox, Hybrid Technologies, DLS, Rainbow, Genesis Audio, Morel
Amplifiers:
Stetsom, MB Quartz, Zapco, DLS, Helix, Brax, Lanzar-Opti series, Audiopipe, Arc Audio, Sundown, Soundigital, Crescendo Audio, Diablo Audio Technologies, Audioque, Digital Designs
Batteries:
Kinetik, XS power, Batcap
I am probably forgetting a few but these will point you in the right direction.