It's a little hard to offer suggestions on such a general topic, but here's some places to start:
If you haven't already done so, read the stickies on the top of this page - there's a ton of advice there. The topic of credit cards has also been discussed before, so searching for "credit card" should bring up a lot of useful results.
In addition to the resources here, also check out
http://www.freefrequentflyermiles.com/index.htm .There's a section dedicated to credit cards, and will give you the basics on the different types of cards.
Without knowing how much you fly and what your goals are (elite status, upgrades) it's hard to give specifics (especially since I don't fly either of your airlines). However, I would say that you should probably concentrate your mileage earning on NW rather than FL. NW miles will give you the advantage of skyteam redemption, and they have a much larger route network. Besides, FL tickets tend to be rather inexpensive, and in general you don't want to burn miles on a ticket that could be purchased cheaply.
Hope that helps get you started