I am curious how much the German Empire spent on its navy compared to its land army? And which sources might be useful to look at.
Oh my YES!
The High Seas Fleet and its construction represented a huge commitment for the German Empire. Rising with the introduction of the Naval Bills in the late 1890's the proportion peaked at about 35% of the defense budget in 1912 down to about 25% in 1914 when the Army fought back and pointed out the increasing likelihood of a land war soon. By then though a program for growing the already large fleet and replacing older ships on fixed intervals had already been established.
In July of 1914 the Imperial Navy represented the 2nd largest fleet on earth, behind only the Royal Navy. The arms race triggered by the launch of HMS Dreadnought had done much to raise tensions and animosity in Britain about German naval ambitions. Just as authors like Tom Clancy wrote about Soviet attacks in the Cold War, British authors in the 1910's would write about a surprise German invasion. The fears of Britain losing naval superiority, the underpinning of her global empire and power was enshrined in the famed "2 Power Standard" whereby the Royal Navy would be kept able to fight and win a war against the next 2 largest navies at once. While this was only ever a rough fit and eventually done away with, in July 1914 the RN had a total of 29 Capital ships to Germany's 17. However tension between global need for the ships and keeping a sufficient force in home waters to fight the High Seas Fleet would never abate through the war.
To understand why Germany launched such a project we need to understand 2 key personalities. Kaiser Wilhelm II and Alfred von Tirpitz.
The Kaiser as much as we can know his heart 100 years on never set out to build a navy to defeat the Royal Navy, indeed here we can truly say that mimicry was the greatest form of flattery. He loved the Royal Navy plain and simple, he just wanted one of his own to appeal to those sensibilities ingrained in his upbringing in England under the reign of his grandmother Victoria. His Chancellor von Bulow once remarked that his greatest dream would be to sale into the Solent with his great gleaming line of battle astride the bridge of his flagship in the uniform of a British Admiral. There he would be received by the equally resplendent British line with his cousin, nephew, or whoever might have been monarch then atop their flagship in a German Admiral's uniform. Then they would anchor off Portsmouth for a grand review and spend the week feasting and toasting and having competitions and regattas off the Isle of Wight. That I think speaks as much to why Germany built her navy as any additional desires to enhance and protect her upstart global empire.
Into this picture then enters Alfred von Tirpitz who would serve for years as Naval minister and just as Bismarck was the father of the German state, Tirpitz was the father of the German Navy. Another German whose primary education and even professional development had come in England surrounded by the glorious legacy of St. Vincent and Nelson. Indeed in the early days of the German Empire her embryonic navy would as likely to be found at Portsmouth as Kiel and to have been outfitted by Armstrong or Vickers as Krupp.
But Tirpitz was a driven man, and works such as Mahan's The Influence of Sea Power on History left a deep mark on him. He was able to help capture the imaginations of a nation and her fickle Supreme Warlord with the promise of a navy that could guarantee her place as a great and powerful nation and an equal share of the valuable colonial ventures that would then be well protected. Thus we have the origins of the Naval Bills that would fund the building of what would ultimately be a first rate force from almost the ground up.
A wonderful read on the naval aspects of the first world war for a first place to start is Robert Massie's Castles of Steel.
For a more in depth look at the arms race and tensions it caused and the ships it spawned you might consider his other work Dreadnought or Arthur Marder's From Dreadnought to Scapa Flow though it is mostly focused on Britain in reaction and opposition to Germany not Germany itself.