3-way floor speakers or 2-way floor speakers plus a subwoofer?

It's all about quality, not quantity. Until you get to around the $1,000/pair range, you are generally best off with a two-way system. You end up with a two decent drivers, well-designed crossover and a rigid cabinet. For the same price, a 3-way system will have more compromises: It has one more driver, a more complex crossover network, and more manufacturing steps, but for the same money, so more shortcuts have been made.

Frankly, a good pair of speakers does not need a sub-woofer for music reproduction, unless you listen to a lot of classical organ music. Quality speakers will do a good job with the entire musical range. The role of a sub-woofer becomes important for home theatre use, because you are now reproducing sounds lower than the musical range: earthquakes, explosions, dinosaur footfalls etc. So, if you want to gradually build up a good system, concentrate on the front stereo pair, and perhaps add a sub-woofer later.

One brand that has always impressed me is PSB Speakers, mainly made in Canada. My system is "over the top" to many people, but I use what used to be their top model, the PSB Status Gold i, for my front pair, run by a stereo power amp that puts out over 350 watts RMS/ch. I have PSB in-ceiling speakers for the rear channels, and McIntosh centre speaker and sub-woofer, powered by two more stereo power amps, the smallest one being a little over 100w RMS/ch. Works for me, but 100 music fans would spend their budget 100 different ways--you have to choose what makes YOU happy.

3 Way Floor Speakers