1. Kenwood is a bit mediocre. It might not even make 900 watts...
2. Power acoustik is complete junk, flea market equipment. The amp would definitely not make 1700 watts.
3. The alpine is a much better choice, they are underrated and much more reliable than a power acoustik... Also, check out kicker amps! They can be had pretty cheap on ebay. A zx1000.1 or zx1500.1 would fi the bill nicely.
4. No, you do not need a battery. You already have one! The amp is powered by the alternator when the car is running, so the battery means very little unless you are going to be playing the stereo with the engine OFF for long periods.
5. What kind of box is the sub in? Definitely go ported if you want maximum output. The website lists the sensitivity as this "SPL: 83.50dB". Meaning this sub is pretty darn ineffficient.... and needs a lot of power to get moving good. Would be better off with a more efficient sub.... From what I can see, many people overpower this sub, as they beleive it is rated very conservatively.
Also, upgrade your big three wiring as seen here.
http://forum.sounddomain.com/ubbthreads.php/ubb/showflat/Number/312025/page/1