Rust and Go are different tools that are good at solving different categories of problems. Additionally they are both languages that will provide different lessons about modern programming ergonomics.
If you expect your programming career to be solving more high level "enterprise-y" problems like writing APIs, web services, and middleware, learning Go is probably going to be more useful to you.
If you think your programming career is going to be more low-level like programming operating systems, libraries, or drivers, learning Rust is probably going to be more valuable to you.
There's huge amounts of low-level systems code written in Go; for example, gVisor reimplements most of the Linux kernel in userland. Go is also the dominant language of the container ecosystem.
You're unlikely to see Go kernel modules any time soon, so if kernel hacking is where you want to to, Rust is definitely the right way to get there.
Placing emphasis on correctness sounds like a plus. How does Rust do this? Does it only apply to memory management? For added performance I could live without gc, but I still prefer it.
Rust encodes object lifetime into its type system, and enforces constraints on how references are used through the borrow checker. With Rust, you don't need a GC. Object lifetimes (not just memory!) are automatically managed through static lifetime analysis. Time and CPU spent in a tracing GC is simply lost, it's emitted as waste heat. In Rust you can reclaim some of that back, and still use a programming style very similar to a GC'd language.
Remember: static beats dynamic, every time. Time spent checking assertions at compile time pays for itself many times over in time spent debugging these same issues at run time. Just as static typing is a huge win over dynamic typing, static lifetime analysis (Rust memory semantics) is a huge win over dynamic lifetime analysis (GC).
I think it's probably rarely the case that static analysis beats GC, and this "static beats dynamic" rule probably doesn't generalize as well as you think it does.
You can learn go in a week, and be proficient quickly. You will find you can read pretty much any go code written by anyone. The source to everything is available.
Rust is more like c++. It contains not-so-easy concepts dealing with memory that require different approaches. It will take 6 months or more to get there.
Rust and Go are different tools that are good at solving different categories of problems. Additionally they are both languages that will provide different lessons about modern programming ergonomics.
If you expect your programming career to be solving more high level "enterprise-y" problems like writing APIs, web services, and middleware, learning Go is probably going to be more useful to you.
If you think your programming career is going to be more low-level like programming operating systems, libraries, or drivers, learning Rust is probably going to be more valuable to you.