This is going to be a bit unconventional, but since FM is important and you said you have poor FM reception in the area, you may want to consider a vintage receiver. I have an old Sansui 2000X (paid under $150 for it), and it has the best FM reception I've seen. Completely blows away my brand new Pioneer AVR in FM reception. Back then (late 70's), FM radio was much more important that it is today, so it makes sense that receivers had good tuners. This little guy even has better reception than a much more expensive Pioneer receiver from the same time period.
You could pair something like that with some small bookshelf speakers, throw an RCA to Stereo Mini cable on the AUX input (for the iPod), and you'll be all set.
I'll be retro-cool looking, have the best FM reception you can get, and play the iPod just fine.
Have a look on eBay. Or PM me, as I was going to be putting mine up there eventually anyway once I move in with my GF.
Panasonic TC-P60ST60, Pioneer SC-1523-K, Oppo BDP-103D, Pioneer PL-550 + Cambridge Audio Azur 640P, B&W CM1 (fronts), B&W CM Centre, Athena Point 5 Mk II (rears), Hsu VTF-2
Sony 34XBR960, Onkyo TX-NR414, Sony PS3, Athena Point 5 Mk II (center and fronts), Wharfedale WH-2 (rears), Polk PSW10