The theory that all small sub are tight and punchy, or that all large subs are boomy/inaccurate is largely just a myth now a days. In the correct enclosure the 12 with likely play just as deep, and the 15 would play just as high(being as must Subs are crossed over at 100hz or less). I have a 18" SSA Xcon in my Suzuki- and it plays everything up to my x-over point(80hz) just fine.
With that said- determine the room you have and buy the largest woofer that will use that space optimally. Also- in a proper enclosure(notice the theme here), the larger sub will be louder watt for watt.
I would suggest a 2nd battery over a 'cap'. Caps that are large enough to really help cost about as much as another battery. For the power you are needing to run(1000w or less) I would recommend doing the big 3, and maybe a AGM Battery/or 2nd Battery. I bought into the Cap thing yrs agao, and rand a 30 farad Stinger in a 1000w build- it didn't seem to help much at all.
I am running a blue top Optima in my Zuk with 1600w rms and it rarely goes below 13v. But I do have a 160amp Alt to replce the lil 80amp stocker. For my Avalanche- I have 4000+rms on hand(Crescendo Amps) to power a pair of 15's, for my electrical- I plan to run 2 Stock size AGM's and a 320 amp Alt. You can only make as much power as you supply.
If you need help with box design, hit me up. I Also suggest checking out
www.ssaudio.com, their forum is a wealth of real knowledge an myth debunking.