Want to learn Daf Yomi in English? Excellent! Here's some resources to get you started:
Start here: What Is Daf Yomi and How Does It Work?
Halakha.com (free PDF versions of the Soncino Talmud - not "modern" English)
Kindle versions of the above
Artscroll Talmud in English
Steinsaltz Edition of the Talmud Bavli
Koren Edition of the Talmud Bavli (updated and expanded version of the Steinsaltz)
Shiurim that are friendly to beginners
Rav Etshalom's Daf Yomi shiur (15-20 minutes on average)
Daf Yomi by Rabbi Dov Linzer of Yeshivat Chovevei Torah (approximately 50-55 minutes)
YU Torah (many speakers, some easier for beginners than others - learn who you like)
Real Clear Daf
The OU has several shiurim and resources by different rabbis, but I found them to be heavy on yeshivish and technical terms
Please send me your recommendations of Daf Yomi shiurim that are easy for beginners to understand!
WebShas: Topical index of the Talmud
Books typically used to study the Hebrew/Aramaic version
They might still be useful to you
The Practical Talmud Dictionary (aka "The Frank")
Dictionary of the Targumim, Talmud Bavli, Talmud Yerushalmi and Midrashic Literature (aka "The Jastrow) - You'll want this edition, which has clearer print and a slightly bigger font.Brown-Driver-Briggs Hebrew and English Lexicon/Dictionary (aka "The BDB") - This is Biblical Hebrew, but it comes in handy.
Reference Guide to the Talmud by Rabbi Adin Steinsaltz (highly recommended)
Aiding Talmud Study by Aryeh Carmel
The Ohr Somayach Gemara Companion by Dovid Kaplan
Books for English learners (in no particular order)
The Essential Talmud by Rabbi Adin Steinsaltz (I really enjoyed this book. He has authored many, many books.)
Learn Talmud: How to Use the Steinsaltz Edition of the Talmud by Judith Z. Abrams (general introduction followed by study guides for some interesting passages as examples)
A Beginner's Guide to the Steinsaltz Talmud by
Understanding the Talmud: A Systematic Guide to Talmudic Structure and Methodology by Rabbi Yitzchak Feigenbaum
Invitation to the Talmud: A Teaching Book by Jacob Neusner (he has also authored many, many books)
Learn Talmud by Jacob Neusner (a review on Amazon says it is aimed at children but still useful for adults)
You might be able to find these books cheaper used or in older editions.
Yes, there's an app for everything.
iTalmud, not cheap but a lot cheaper than a Shas set (a review by Dov Bear)
Real Clear Daf, free as of Oct. 5, 2014