What packages/interfaces in the standard library should I study first?

io and io/ioutil and the reader/writer interfaces look like they come up often, what else?

net/http for high level interfaces, net for high level abstractions over low level interfaces.

time: commonly used. Surprising uses of channels and goroutines.

os/exec: how to run a subprocess.

net/http, sync/waitgroup, time, and os 

If studying to learn, better to write a program that would need to use the parts you're interested in. In general the standard library can be simple to follow for pure Go packages, io related packages are examples of this (bytes, bufio, io, etc). But the std library itself has a lot more complexity in many areas than you will find in every day user space code for various (unavoidable) reasons. 

Best to just find a project you can work on that will lead you to learn the packages first hand. If you want to look at a package as an example of good go, look at the io package. It defines the reader and writer interfaces, which are used throughout the other libraries, along with some implementations of them and usage of them, which help to exemplify the idea of interfaces in go and how small, simple interfaces can be very powerful.

Package io https://medium.com/go-walkthrough/go-walkthrough-io-package-8ac5e95a9fbd#.smdwi7h7b