2000 Corolla, Step up from factory speakers

OK.... I just replaced the factory AM/FM/Cassette (remember those?) in my 2000 Corolla LE with a Pioneer DEH-1600 AM/FM/CD.  (Please, no flames about this choice-- for $45 NIB from WalMart, I couldn't turn it down).  Needless to say, the OEM speakers have got to go. At 50W X 4, they would probably fry in no time, and well- to put it bluntly- they sound terrible. I'd like to replace all four with a nice sounding set of  2- or 3-way speakers. (One question I have... do these 2- or 3- way setups have a built-in crossover... never see any mention about a crossover network in any of the ads or specs)

I am *NOT* interested in getting massaged by the thumping bass that you feel and hear from 1/4 mile away, and I have no desire to go the sub and amp route anyway.  I just want a clean, natural sound that I can turn up loud enough to drown out the highway noise and listen to CDs.  I believe both the front (doors) and back (deck) are 6.5".  I don't want to spend top dollar, but I don't want junk either.  Any recommendations? 

50w x 4 is a peak rating, which a head unit will not produce- realistically, most decks will only put out roughly 20w per channel.  Yes, 2 and 3 way speakers will have built in crossover networks.  These are different than component speakers, which have separate crossovers.  The best thing to do is to listen for yourself and buy what you like.