What is the proper amp for me? Details inside

I have a 2007 civic lx sedan. The sound on the stock system was poor so I upgraded all four speakers with polk audio's db650 since they were cheap and good ratings all over. I noticed that the sound is clearer now, but I am probably getting no where near the full potential since I didn't put in an amp. I've bee told that the car's factory stereo is 160 watts max and around 80rms. So I am guessing this means it's divided by 4 so 20 watts rms and 40 watts peak to each speaker. These are the stats of the polk speakers - Power
RMS power handling (watts) ?60
Frequency response (kHz) ?40Hz - 22kHz
Peak power handling (watts) ?180
Recommended amp wattage range0 - 199
Peak power range (watts)150-249

The couple questions I have are what do you think a good amp will be for these stats that is not too expensive?
With the appropriate amp will I noticed a huge difference since it looks like I am currently get 1/3 the rms power per speaker and 1/4 the peak power if I am not mistaken. (is that right?)

Also, Crutchfeild said I should wait about a week before judging the speakers because it needs time to warm up on moderate levels. Does this sound right, maybe I will notice a difference in a couple days. Any help about the proper amp for short money is appreciated it. Then I need to worry about paying to have it installed. Will I still need to buy the wire kits if it's being installed into the factory receiver. Looking for an amp that is inexpensive, but can handle the power and the possibility of adding a small sub maybe down the road. Thanks for you help, I am new to this if you couldn't tell.