OP, for the most part you are not going to hear a difference even if you spend $1000 on the door speakers if you are still amping them with a headunit.
a decent set of speakers (that will do what you are asking) are going to have an RMS of 75w or higher. A stock headunit probably puts out 10w RMS and even a $400 aftermarket is only going to give to a MAX of 22w RMS.
Also how loud is your sub when volume is at your normal listening level. Depending on how loud your sub is there is NO REASON to change rear speakers because the sub is pulling all bass away from them anyway and the little bit of mid and high sound that is left is thus drowned out by the excessive bass of the sub.
If you want your front sound (or stage as it is called in car audio) to be plenty loud and clear buy a decent set of 5.25 or 6.25 components then buy a used 2 channel amp from CL or Ebay (just dont get the crap brands)
these bad boys are B-Stock and generally more expensive (B-Stock means there is some sort of cosmetic issue which doesnt matter in your case since you shouldnt be able to see them anyway)
Shop CDT Audio - CL-60
if you bump your budget to $250 getting the above component set will leave enough to get at least a "decent" quality amp
WoofersEtc.com - PMA6002F - Alphasonik 2-Channel 500W RMS Class AB MOSFET Amplifier
alphasonic makes decent amps and this being a 500w Class A/B amp should really get the job done for the CDTs i linked above.
Also if you are willing to buy used check out these groups on Facebook, you can post a small description of what you want and your budget and get a TON of offers and advice from people whose 1st passion in life is car audio.
https://www.facebook.com/groups/246585605413072/
https://www.facebook.com/groups/388436331210782/