Okay, because I can talk about this subject with a degree of legitimacy now.
I remember reading some sort of 'guide to graduate study in economics' a year or so ago, written by some people in the UC system. I don't really remember much, except one line. "In grad school, you are judged by the fruit, not the sweat, of your labours." Okay, I'm paraphrasing a little, but that's pretty close. Ir's incredibly true.
Don't stay up until 5am trying to fix your code so the robust standard errors on your weird model match up with the textbook's to the fourth decimal place when the first two already match. It's just not feasible to do everything and remain sane, so setting priorities becomes extremely important. You don't want to become the person who lives out of their office working 90-hour weeks. Memorizing the proof to show that the set of essential finite games under the sup metric is residual is just not worth it.
In particular, a crucial lesson I'm still working on learning is being able to put a wall between economics and leisure. I remain terrible at resolving to take the morning off and put in a decent rest of the day. Often I will just blankly click around the internet until lunch while fretting about what work I have to do, at which point I start an internal debate on whether I've taken any time off. This is not a good way to spend time.
Okay, math. The importance of mathematical preparation decays throughout the first year. There were very few new mathematical techniques introduced in the second semester. (Though the first micro II class was a little freaky when the prof claimed the Riesz representation theorem was "standard off-the-shelf" stuff we should know.) The first term, preparation helps you a lot. Math for economics, mathematical statistics, Bellmann programming. If you've seen them before, it makes a big difference. I can show you my <50% on the mathematical econ midterm early last October for proof.
What is much more important than being exposed to lots of high-level techniques is 'mathematical sophistication'. This gets thrown around a lot and it's hard to define. Conditional on being told "use a second-order expansion here to derive blah blah blah", it's not difficult to mechanically go ahead and solve. But staring at a problem you've never seen before under severe time constraints, the real skill is to recognize that a Taylor expansion is the preferred method of attack. (And since any problem on a final exam has probably not been seen before...)
Yes, this is correlated with exposure to high-level materials, but not perfectly. I don't know how to acquire this talent, and it's not something I'm particularly great at, but it's crucial. Being really comfortable with the material at the level of Rudin is a lot more important than having been in a course that worked through a lot of weird results in functional analysis.
After this, everything else I could talk about becomes a lot less important and/or obvious, if what I said already wasn't. Stay as healthy as possible. Spend as little time thinking about money as possible. Don't be a moron in social situations with your classmates. Try to remember why you're doing it all in the first place.