Reconciling Ministries: This is My Story
Reconciling Ministries Network has a web-page filled with the stories of LGBTQ United Methodists.

The Reformation Project: Biblical Case
The Reformation Project has a short, ten-point summary of the arguments for full inclusion that features a short video from Matthew Vines.

Books
Matthew Vines makes the same arguments above in more detail in his book, God and the Gay Christian: the Biblical Case in Support of Same-Sex Relationships.If you finish that and want more, you might consider Changing our Mind by David P. Gushee. Be sure to look for the third edition which includes a transcript of the excellent speech, “Ending the Teaching of Contempt.” Looking for a Wesleyan perspective? Try Holy Love: A Biblical Theology for Human Sexuality by Stephen Harper.

“For the Bible Tells Me So” Documentary
One easy way to explore LGBTQ inclusion for yourself and possibly begin a discussion in your church might be with a viewing and discussion of the 2007 documentary “For the Bible Tells Me So.” The Human Rights Campaign has a free discussion guide at the link above.

Faithful and Inclusive—the Bible, Sexuality, and the United Methodist Church
A six-session, DVD-based study from the Richard and Julia Wilke Institute for Discipleship at Southwestern College.