The use of Rust is rising, especially for new systems level projects or rewrites of older programs. This is especially true where unexpected issue reduction is a high priority (high frequency trading systems, industrial systems, security systems, video transcoding, packet switching and routing systems, video monitoring systems, virtualization and emulation, web servers, other embedded etc.)
I would recommend getting started learning Rust by having a few projects. I would recommend starting off by building a multi-threaded web server. https://doc.rust-lang.org/book/second-edition/ch20-01-single... See how many concurrent clients it can handle and make adjustments to increase it's max capacity. After you have done that I recommend building your own daemon to handle log parsing and analysis from your web server to give you a nice table of stats. To spice thinks up I would recommend trying to do this without the dependency on external resources after you have downloaded all the resources you need: https://doc.rust-lang.org/cargo/reference/source-replacement... https://crates.io/crates/crates-mirror then try to build the projects.
You can also do some much needed checks on your programs input by using Valgrind and several other tools. Once you are satisfied with your program insure you use Rusts tools to also build the documentation and check your coverage: https://github.com/huonw/travis-cargo