Wow! Thanks for all the responses so far. My interests range from motorcycles to mandolins to beer making, and it seems that the internet has become a home for all like minded people pursueing their hobbies.
I guess I will try to clarify things a bit. As I said, I play guitar and mandolin. I can play chords on both and play anything that uses basic chords, and particularly on the mando, I've figured out (with the help of tabs and slow down software) playing the actual melody for some songs. I have a basic understanding of how to read a staff of music, just nothing close to sight reading. I don't have an aversion to learning it, its just that with the guitar and mandolin, I've been able to play most of what I want to play using chords or finding tabs.
As far as what I want to play, I love Irish music. Stuff like the Pouges, traditional stuff, jigs, reels, etc. Thats mostly what I use the mandolin for. Beyond that, I guess things like hymns, the occasional pop / rock song that has a nice melody, Christmas music, slow stuff. That is what I'm likely to wind up playing.
What I'm looking for in an instrument is something that won't break the bank (since I just play to amuse myself, friends, and family). I love the sound, and I think I'll really enjoy the concertina, so I want to get something that won't limit me in a year, but I'm not looking for a professional instrument. Just something that sounds decent. As far as English vs Anglo vs Duet, I humbly submit to your guidance as things like "cross fingering" don't mean anything to me.
Oh, and one more thing, can one play chords on a concertina?