Supplies you'll need for the instrument rating

Instrument Flying Handbook

This book should be your starting point for your IFR training. It will cover the basics such as how the pitot-static system and gyroscopic systems work, how to properly scan the instruments, IFR maneuvers, and human factors related to IFR flying.

Instrument Procedures Handbook

The Instrument Procedures Handbook goes more in depth with the procedural portion of instrument flying such as how to properly depart an airport, how the en-route phase works, and what steps to take to get back on the ground.

FAR/AIM

This one should already be in your possession from previous training. Be sure to get the latest version, though! The FAR/AIM is on an annual release schedule, and can be obtained from various different companies who each have their takes on formatting, illustrations, etc.

Terminal Procedures Publication

The TPPs contain all instrument departure, arrival, and landing charts in the region the TPPs cover. Be sure to get the TPPs that are relevant to your area.

IFR Low Enroute Chart

Just like you need a sectional chart for VFR flying, you'll need a chart for your IFR ventures. For the purposes of flight training, the low enroute chart is all you'll need, but there might be testing on the high enroute chart if you're working on the airplane rating.

Chart Supplement

Where do you look to see if an airport offers fuel, or who to call to hear if the fuel farm is working? The chart supplement is the official source you'll want to rely on for the checkride. In addition to this, the chart supplement contains a list of preferred IFR routes, locations for VOR receiver checks, and more.

Instrument Pilot ACS/PTS

Read this cover to cover. Knowing the conditions the examiner is testing you under is crucial, and will help you immensely during training. This booklet also serves as an excellent study tool, as every single subject the examiner potentially will have to put a check mark in is written in the ACS/PTS.

ASA Oral Exam Guide: Instrument Pilot

A complete list of common questions and scenarios asked during the oral examination found in the Oral Exam Guide. It's comprehensive enough to give you an idea of where you need to be, but should not be a source of information to solely rely on, as it mainly gives you rote memory knowledge.

Aviation Weather

One of the most undervalued topics in flight training is weather. It's essential that you read and understand basic weather theory if you're looking to succeed in this field long term. The majority of aviation related accidents are due to weather and human factors.

Aviation Weather Services

Understanding the weather theory is one thing, but understanding how to apply this knowledge using weather reports is a whole other thing. This book goes in extreme depth of aviation weather reports. It's important to remember that the FAA is currently in the process of reorganizing a lot of older aviation related weather tools for graphical tools.

Bonus: Jeppesen Instrument/Commercial

This Jeppesen book can actually substitute the Instrument Flying Handbook and Instrument Procedures Handbook. The reason this book is not at the top is because it doesn't come directly from the FAA, and it has a higher cost than its competitors which are free of charge.