The sad part about your build is, what you need to do is figure out what electrical is going to be in your budget. I don't think you will get to where you need a second battery on that budget, but if you're adding a real sub, you will need to upgrade your alternator.
You need to figure out what upgrading your electrical is going to cost. About $40-$80 for the BIG 3, and you need an alternator.
Lets say you get a 1,000w amp for your sub.
1,000w / 80%( or .8) for amp efficiency is 1250 w draw (by your amp to push out 1,000w).
1250w / 14.4v = 86.8 amp draw for that amplifier.
Your stock alt is probably around 100amps, and that is enough to do everything it may need to: electric fans, efi, AC, headlights, turns, horn, and some other stuff.
YOU NEED TO SEE WHAT YOUR UPGRADED ALTERNATOR OPTIONS ARE, AND WHAT IS IN YOUR BUDGET. This could be anywhere from $150- $600. This might eat up a large chunk of your budget, and I always suggest planning out the entire thing, before you buy anything, unless you get a really smoking deal on something, so you can adjust if you need to.
For alternator shopping you need to know two things:
Output at or near idle, &
RPM needed for full output.
I'll bet in a honda you rev higher than a v8, and so this might open up your options, but you need to know what it will recharge while you're sitting at a light, and what speed/rpm do you cruise at, and is that above your full output.
If you can find an alt that is 40 amps higher for next to nothing, then you have about 500w you add, and when it's playing full volume, with a constant draw, (which subs don't do), then you couldn't possibly have a problem. You can still go well over this number. If you find one that is 150 amps higher than stock, for just a little more, then you have room to play with.
I always recommend looking here for deals:
WoofersEtc.com - The Online Car Audio Superstore, the Largest Selection at the Lowest Prices!
www.woofersetc.com
(they owe me some commission by now).
I would bet that with a real sub, your front speakers and the amp will be 1/3-1/2 your budget. There are also several things along the way you could upgrade later. Sometimes you can find nice deals on Clist, or FBook marketplace for enclosures, and even package deals on a system.