This is such a great endeavor for your student and your school, especially as 81% of LGBTQ youth in the United States reported there being no positive portrayals of LGTBQ people, history, or events. In fact, 15% reported learning negative portrayals (GLSEN, 2013). Across the country, less than half of all students reported they could find LGBT related content in school library.
There are some great starting grounds for content/history, which might help to direct your student toward specific book titles for purchase:
GLSEN
Human Rights Campaign
The Safe Zone Project
Teaching Tolerance
The Trevor Project
Your Community/Your School
This site would be a great start too: https://libguides.luc.edu/c.php?g=49784&p=2764896.
To Ken's point about funding, a lot of organizations will match whatever donations are collected. There might be mini-grants available too, etc.