Maybe you should invest in a nice sound system.
Many people consider the OEM sound system to be crap but it's usually because the BOSE amps have started to fail so the audio quality is not what it should be. I'd encourage you to search out a Prime'r near you that has recently replaced the amps and listen to the sound system as its best. Best if you find someone who has also added the SOS ipod adapter too. I find that today's songs tend to have a lot more base than songs of just 10 years ago.
Then, if you don't think the sound is good enough for you .. and you're determined to spend some (more) hard earned cash, let's consider the sub you just bought. That sub enclosure is intended to replace the existing one which is a combo amp and speaker ... there's no real way to keep the existing sub amp and use it to drive the new sub .. and it wouldn't have the power to do it anyway.
So, the next logical, cheapest step is to go to a central amp design; keep the OEM head unit; bypass and make do with the existing speakers; and use the new amp to power your sub. This is going to probably be at least $500-600 if you buy an installation kit and do the work yourself. Again, one misconception is that the door speakers are probably blown but it's almost always the BOSE amps that are in the integrated door unit. So, by using your new central amp and bypassing the BOSE amps, you should be ok with postponing door speaker upgrades until later. Your biggest budget cost will be the amp and the cost will depend on brand; number of channels; watts per channel; etc. Simplest place to put it will be behind the drivers seat on the bulkhead .. short wiring runs and only the power wire needs to go through the bulkhead but the fuse box in the engine compartment is close.
The above suggestions get you going with power for your new sub and will also allow you to bypass the cost of upgrading any of the BOSE amps. However, if you're one of the small percentage of people whose head unit is starting to fail, you can send it to BrianK and have him fix the bad capacitors or if you still have some money burning a hole in your pocket, the next investment people seem to make is to upgrade to one of the current designs which has integrated video, audio, gps, etc. These can also add probably at least another $500 for the unit plus you'll need to replace your console with one that will accommodate the 'double DIN' (ie. larger size) so that will add cost as well .. even more if you decide to do something in carbon fiber. Plus you'll need adapters to make it fit, etc.
If you've been on Prime for a while, you may have heard the performance junkies talking about the 'go fast crack pipe' but I maintain that there's also a 'sound system crack pipe' as well. And there are always those who ask the question why you'd want to spend a lot of money on something that interferes with .. or can't be heard well over the engine/exhaust. So you be the judge.