Googling around, I can find many examples of this question, but they are all dated before the move to Vulkan/DX12, which I've heard has represented a big paradigm shift.
Are the old recommendations still relevant? Or are there newer books which are more relevant to someone looking to get into the field today?
A lot of the theory from classic books is still valid, so even a copy of Computer Graphics: Principles and Practice will look fine on your desk. "Real Time Rendering" by Moller/Haines and "Physically Based Rendering" by Pharr are excellent. "Game Engine Architecture" by Gregory and "Mathematics for 3D Game Programming and Computer Graphics" by Lengyel will probably prove very useful and relevant to you as well.
Online resources, the free https://learnopengl.com/ and the $10 http://graphicscodex.com/ are both fantastic. Make sure to read https://fgiesen.wordpress.com/2011/07/09/a-trip-through-the-..., and also study the techniques used for the craziest entries in https://www.shadertoy.com/
And then, lots and lots of papers and presentations from the past 5 or 10 years of Game Developers Cconference and Siggraph.