Where to start in upgrading?

I have a basic home theater system with a 2010 Pioneer A/V receiver. I am using some old Fried A/3 bookshelf speakers for the two front monitors, along with a Klipsch subwoofer. The source is either an Ipod, a cheap CD player, or internet radio, which is what we listen to the most.

I would like to start upgrading the two channel part of the system. I don't know where to start: new speakers, a separate amp, the source, or something else? I have a fairly good sized room. (Marital issues will require that I stay with bookshelf speakers and a sub.) We tend to listen to music at a fairly low volume. I like the sound of the Frieds, but I want to improve it. I recognize it will be a process, and I expect to buy used equipment.

I note this question has already been addressed very well here: