I'm pretty new here myself and I was recently going through this analysis and considered many cards. I decided to go with the American Express rewards green card as my primary card.
There were many reasons for this choice. Like many mileage cards, I receive 1 Membership Rewards point for each dollar spent on the card, which is what it seems most airline cards give you. The advantage here, however, is that these points can be converted to FF miles on just about any airline I would consider flying so I am not restricted. Moreover, this card gives you 2 MR points per dollar spent at supermarkets, gas stations and wireless cell phone bill. So that's a plus over airline cards for me.
Before choosing a card, you have to consider what you primary goal in getting rewards is - that is, which airline you would like rewards with, etc. Since I live where I can use EWR or JFK airports (both big hubs for some major airlines and pretty competitive markets), I decided airline awards tickets aren't worth very much to me. Thus, my goal is to try to obtain Hilton HHonors points. In my opinion, Amex is a great card for such a thing.
I admit there are a few disadvantage to the Amex green card. The signup bonus for my card was 5000 MR points, which isn't as big as some airline mileage cards. Also, the annual fees, from what I've heard, are pretty hefty - I don't know exactly, but maybe $60 - $80 or so. I was pre-approved for this card and got it fee free for one year - it may be possible to get the card fee free for a year if you go to the website or call.