Learning Linux is a widely various task. Have you had any background in Unix type systems? Will this be a dedicated fileserver? Will it be running on a wired NIC (some wireless interfaces are a PITA with Linux driver support)?
In terms of how streamlined your server could be, it also depends on what else you might need to do with the machine, and also if you need a GUI. Running a Linux kernel on your hardware shouldn't be any problem. You could quite possibly run a dedicated server installation, without any of the usual desktop/workstation features. It depends on what you are comfortable with, though. I think using a more fully featured distribution may be easier for you to come to terms with the system.
You could try learning a bit about Linux with a virtual installation somewhere, or with a live CD/DVD on your server hardware, just to get used to it for a while.
This is a text which I found handy when first learning to use Linux based systems. From memory, I don't think it goes into running a file server. However, it's not bad for getting started.
