Sorry, I didn't see the question until now. I first read about first-order formal languages, "structures" and what it means for a set of sentences to "logically imply" another sentence, in Enderton, and in Rautenberg. I don't think either of them is really easy to follow, so it was really helpful to have access to both. Then I bought Kunen's book "Foundations of mathematics". That's a very good book, so I can recommend it without reservations. But I got the feeling that a lot of the stuff that I found easy to understand would have been quite hard to understand if I hadn't read the about the stuff I mentioned above in Enderton/Rautenberg first.