battery being drained

1999 Buick Century

So, that's what is in my car.. it's got the stock alternator and oem battery. I've had the system in my car for about 8ish months now and haven't had any problems with it until recently. Every once in a while I'll go out to my car and it'll be dead. Thinking this wasn't a big deal in the first place I got in the habit of bringing along my booster pack just in case it should ever happen again. After that the car would start flawlessly (no major difference in listening habits) for another few weeks, then the car would go dead. After recharging the battery the car would start and run fine for another few weeks,then die again. This routine has kept up since. So I got the idea (from a mechanic friend) to unplug the cable running to battery positive to see if that had any affect. It did, my car hasn't died in the 2 weeks its been unplugged.  My question(s) is(are), does my alternator not put out enough amps to keep my battery charged? Is my cap too small? Should I upgrade the battery to a Optima (or comparable)? Should I look into a dual battery setup? Did I harm my cap in any way by unplugging it/will I need to "charge" the cap before reconnecting the system?

I'm a pretty big 'newb' when it comes to the car audio installation world..So any comments/suggestions would be greatly appreciated... I know I like loud music and had the money to afford the equipment, now I want to get the best out of it that I can. I got this installed at a local Futureshop and who knows if what went in is really what I needed, or what would help out buddy's commission check.

Did i miss something? I would have thought battery right away! He said OEM battery in a 1999 Buick century!

The battery is an OEM replacement, not literally the battery that came with the car in 1999 lol (in case that's what you meant t&t). I'd like to be able to listen to my stereo while the car is off too, but with my current setup if I turn off the car and have the stereo still on (electrics still work with the key off until I open the door) the battery will die in less than 5 minutes worth of low volume listening. Should I eliminate the cap and go for a H/O alternator and 2 batteries with an isolator? Or would an H/O alternator and 1 Optima do the trick? I've already spent close to, if not more than 2 grand on the setup and as it sits right now.. that's just 2 grand worth of metal and wires in my trunk serving no purpose other than to tease me everytime I go for a drive. I'm not overly concerned with cost (music is basically my only hobby) right now so any suggestions help. If I do go for an Optima, do I go yellow top? red top? one red one yellow? lol HELP!