Beginner's text for Algebraic Number Theory

I would recommend Ireland and Rosen's text Classical Introduction to Modern Number Theory. The prerequisites for the first 10 or so chapters are minimal (first semester undergraduate algebra course).

I'm a big fan of Murty and Esmonde's "Problems in algebraic number theory", which develops the basic theory through a series of problems (with the answers in the back). Another nice source is Milne's notes on algebraic number theory, available on his website here.

I would recommend Stewart and Tall's Algebraic Number Theory and Fermat's Last Theorem for an introduction with minimal prerequisites. For example you don't need to know any module theory at all and all that is needed is a basic abstract algebra course (assuming it covers some ring and field theory). But again the first chapter gives a quick review of the basic material from abstract algebra that is used later on.

I have used this book when I took an introductory course in Algebraic Number Theory and the experience was really good. The book has many examples and the pace is not too fast.

Most other books I have seen rely more heavily on module theory to make the exposition more general but since probably you don't have that background yet then I guess that this book may very well suit you perfectly.