Help with a good car audio system?

I’m looking for some decent speakers for my car i was looking at 2 pairs of these: http://www.amazon.com/gp/product/B00A0LZHYS/ref=wms_ohs_product?ie=UTF8&psc=1
and for subs, my brother has 2 10" or 12" subs (not sure exactly what they are but it’s late so i can check tomorrow) and they sound pretty decent i think they just need a different amp because his current amp looks old, I don’t know for a fact if its a good amp and knowing my brother he probably went for the cheapest option… So could someone direct me to any of the following
1.) Better speakers for the price
2.) good amp for speakers
3.) good amp for subwoofer
this will all be going into a 2007 chevy cobalt sedan LS, and if I’m missing any information you need (I’m guessing i am) please ask and i’ll try and tell you the best I can… I’m also currently learning all the wiring behind a stereo system and would enjoy a good tutorial… I would also like to keep everything under $300, thanks so much!

Addition: the subs also make the trunk vibrate a lot when it hits hard, anything that can help this? I’ve been reading and lots of people say peel and seal (cheaper alternative to dynamat) works well, and some say it sucks… Any personal experience here or any other recommendations? thanks again

Dynamat is only $50 and maybe around $70 after shipping. Should really consider it if you are putting in a sound system because the sound system will be worthless, because of both the vibrations of the body and the exterior noise coming into the car.

Funny he set a budget of $300 and then all suggestions even just one part is more than that....