The Songtowers are around 88dB efficient, so I doubt the Ikon will drive them loud enough with 12wpc.
As you already have an amp, I would concentrate on getting a quality signal, cheaply, to the amp you have now, and then refine from there.
I see 2 good options, for under $500.
1 - Logitech unit - SB3 or Duet, your call. I have used an SB3 for years now (mine has been modded by Bolder), and recently bought a dedicated old desktop PC to use wired (ethernet) to the SB3. Dead simple, and cheap.
2 - USB DAC. There are lots of quality units out there, and would allow you to use the s/w combo suggested above to get all that good FLAC out of the PC, avoiding Kmixer, and driving good tunes to your amp.
Though I am very happy with my setup, for the cheapest, fastest way to get going, I would go with the USB DAC. You are likely able to get this done for under $200 including shipping, and cables etc.
Does that fit the budget?
If you find that the combo of your amp/speakers does not please, you can consider other options down the road, and likely resell the USB DAC.
In fact, I would troll Head-Fi for used USB DAC's, there are some gear hounds over there that might be playing around with configurations and be offloading exactly what you seek!