Subwoofer Overpowering Stock Speakers, Help please!

Hey folks,
 
I have a (mostly) stock 2002 Accord. I was recently given an 300w amp with a 300w subwoofer box(2 12 inch subs).
The problem is now I'm finding that the bass is overpowering my stock speakers. I've been told that if I replace the rear speakers with 2 decent 6 x 9's it should help considerably.
 
Do you guys think that should be my first step? And if so, should I invest in a really quality pair of 6 x 9s, I'm on a very tight budget and the cheaper the better while still solving my problem. These are the 6 x 9's I'm considering getting, should I invest in a better pair, or will they solve the problem? Note that I'm using a stock head unit.
 
http://www.bestbuy.ca/catalog/proddetail.asp?logon=&langid=EN&sku_id=0926INGFS10074542&catid=20116
 
I'm kind of a newbie to car audio so excuse my lack of technical jargon.
 
 
Thanks,
Adam
(Also, do you know if this price includes a pair? 2 speakers? Or is it just for an individual speaker)

I was also considering these inifinity speakers:
http://www.futureshop.ca/catalog/proddetail.asp?logon=&langid=EN&MSCSProfile=3C79F0C7EA3162B2B9AD68C2316B6FA1AD6EDE4252852C39EB80FD9EDA4449F02641E4D1621BB8607BBB9276EAE0AE9DB71C3690CAC837081A612530E1500FD8AC54D5E3B88591B7E49CB3FDFE85C4F6CAD4B49A0932D5811F7CDCFFFEF4A24E5A57E239AA6BAA47A56AFF46100C6DDDFD0C2A0917C59FDC&sku_id=0665000FS10063261&catid=11044

When you see speakers on sale, the price is for a pair, unless you are looking at subwoofers.   Out of the two speakers you are looking at, I would go for the Infinity set.  Infinity is better quality than JBL, and since its the same price... why not?  I would really advise you to look at a 3-way speaker instead of a 2-way though. 
 
Upgrading your rear speakers will help considerably, but your sub will probably still drown out your music a bit.  I know mine does, 360 watts into a 10 inch Kicker, and I have 4-way Pioneer 6x9s in the back.

providing the amp is only driving the sub then most amp's have an output level or various other adjustments on them so you can tune it a bit better to work with your system.  That's going to be the cheapest and fastest way to solve the issue... 

I went and bought the infinity speakers, I know you suggested the 3-way, but I wasn't able to find a suitable pair for the price I wanted to pay.
 
Anyway, I'm installing them now but I've noticed that the connector doesn't match the connector that is built into my car. It looks like on the stock speaker there is some sort of attachment that connects the speaker cable with more ease. Should I just cut the wire before this connector, strip it and attach it to the new Inifinity?
 
Thanks
Adam

When I installed my speakers, I just cut the wire, stripped it, kind of braided it together, and then covered it up with electrical tape.