choosing an amplifier for system

My apologies if I come off a little clueless, but this car audio stuff is like learning another language. I just drive a 1998 Dodge Durango w/ the Infinity Premium System (Ironically all the speakers were blown when I bought it. Premium, whatever) and I recently bought new speakers and a new receiver: Alpine Type-S SPS-600's and a JVC KD-R300. From my research, that receiver will power those speakers no problem. If I'm completely wrong, please let me know.  I bought a C10 Kicker Subwoofer a while back (couldn't resist the price) and I thought I had an amp that would power it, though it turns out I do not. Kicker puts out 300w and the Amp only powers 240.  So, before I completely ruin my sub, I need some guidance or words of wisdom as to buying the correct amplifier for the job. I would like to keep the amp as inexspensive as possible, but enough to keep good quality. The Kicker puts out 300 watts with 4 Ohm (ohm is where I became lost when trying to read up about this) so I would obviously need a subwoofer amp to power that. I figured I can just use my 240w amp for the speakers.

Links to speakers, receiver and subwoofer:

Thank you for your time.

This answered all my questions. Thank you very much! I now understand the whole mess about how much power the sub can handle and what amp to use. Thank you for clearing that up. I will use the 240w amp to power the sub and I actually have a 100w amp as well. So, like you said, that should be enough for the speakers next to the deck's power, for a little better performance?

I know the speakers and subwoofer arn't the best in the business. But, the speakers are cheap enough, yet provide better sound quality than others I have compared them to. And let me tell you, anything is better than what I have now. I have to keep my bass turned all the way down just so my speakers don't "fart", not to mention I only have the front door and tweeter speakers equipt. The rear were just too terrible to keep going. As for the subwoofer, it was 45 bucks new in box never been used, can't beat that. Over all, this set-up should produce an okay sound, I'm not trying to win any competitions, haha.

Thank you haemphyst for your help.

Ah. Though I know the deck has a built in amp:  50W x 4 MOS-FET power. Would the 100w amp just a better choice anyways or would it be better to run just deck power?