What were expenses like for a medieval king, or the nobles who served under him? Household expenses, weapons and armor, fortifications, any fighting men they employed, etc...? Which sets of expenses would tend to be larger, and which smaller?
Also, how did they get the money for this? I'm under the impression that the subjects would often pay with harvests and labor. The labor could obviously go towards working on fortifications; the food also could be put to good use, but how did they choose to use it?
Expenses would also go up a lot in wartime, what with the need for soldiers. How much of these extra expenses were accounted for by raiding the treasury, and how much was from demanding extra revenue? And was the extra revenue part of "the deal", or did it have to be negotiated?
Let's say we're talking about France in the 1200s, but if you know about somewhere else or "in general" then don't be afraid to speak up.
This is a far harder question to answer than you might imagine. It wasn't until about the 13th century that we even have strong records showing things like expenses for the French kings, and we don't have all of them. Germany was even worse, because the German kings didn't set up as much of a bureaucracy as England or France did. We have the best and most complete records for England. This comes mostly in the form of the Pipe Rolls, a series of records of the crown's income and expenses that begins in the early 12th century and continues down to the early 19th.
Even where we have records, this doesn't necessarily mean we can get a full and accurate picture of the income and expenses of the crown. There are dozens of reasons for this, but the big ones were that 1) not all of the income and expenses were actually recorded and 2) sometimes the income that was recorded was a projection of what should have been received, not what was actually received. So it's really hard to figure out what the actual cash-flow looked like. Not to mention that a lot of it, as you've noted, did not arrive in the form of cash at all. Despite the problems with our records, we can tell you, even with some specificity, where the money tended to go. We have more records for kings far sooner than we have records for the nobility, and I will focus on Philip the Fair, because he is an especially illustrative case.
Your instinct that times of war resulted in different spending patterns is accurate. For Philip IV the Fair in France, who was king at the end of the 13th century, over the first half of his reign his income and expenses weren't always equal, but they didn't far outstrip his means and he could pay off his debts. The vast majority of his expenses went to wages and household expenses (mostly feeding people and horses). Obviously the foodstuffs received instead of cash would be used for this purpose. Excess could be sold at market or donated to monasteries and the poor. After that were gifts to loyal retainers and alms. Work like repairs on castles, roads, or bridges was also an expense, but it didn't, in the normal course of things, rival that of wages. Neither did the administrative costs of running the government outside of the typical wages paid.
Unfortunately for Philip (and the Jews and the Knights Templar), Philip went to war with Edward I of England in the late 12th century, leading to a huge deficit because the expenses of war far exceeded his income. We can see in Philip how going to war could actually be devastating to a system that was otherwise well-balanced. In order to cover these costs, he first took out substantial loans from the Temple of the order of the Knight's Templar in Paris. Then he tried to recoup this via more traditional means, such as raising taxes. When this wasn't working to clear his debts, he expelled all of the Jews from the territory of France in order to allow the crown to absorb all of their property. When even that wasn't enough, he turned on the Knights Templar themselves, accused them of heresy, had some of the executed, and took their money. Overall, these episodes have left Philip with a very bad reputation.
Now, what kinds of amounts are we talking about? During this war with Edward (part of the 100 Years War), one of Philip's main financial officers made payments of 239,842 pounds for arms, payments to troops, and other expenses. Another made over 430,000 pounds worth of payments, and a third spent nearly 170,000 for the war. There were countless other smaller figure paid, as well, making the cost of this part of the 100 Years War close to a million pounds for the French crown.
Compare this to the stable years which came before. Philip collected his rents from various regions at the ends of the seasons, and they tended to be relatively stable. He received about 110,000 pounds from Normandy every year, and similar amounts from various other areas of his domains. At the same time, he borrowed heavily from the Templars, owing up to 300,000 pounds at once! However, he always paid off his debts, and sometimes the Temple actually owed him money. He was living within his means, even if he wasn't living frugally. The huge additional expenses of the war, without built up cash-reserves or the ability to successfully increase his income, is what did Philip's finances in.
The main source that I used for this was JR Strayer's The Reign of Philip the Fair. Strayer's book on the development of government in the Middle Ages, On the Medieval Origins of the Modern State, is also illustrative of some of the sources for tracking finances that are available.