Many challenges incorporate some kind of Linux challenge. I have tried several versions of the OS myself, and recently have found Knoppix to be an interesting version. Knoppix boots from a CD and so there is no need to mess around with boot partitions, disks, etc. Dont expect it to be quick, its just useful for the occasional foray. This is not to say that most Linux challenges actually require you to use Linux, but rather to demonstrate some knowledge of the OS.
Many challenges have some kind of emulation of a Linux command prompt, just like the DOS prompt in many respects only we use different commands there. First of all if you are asked to log in; if you do not have a username then guest/ anon/ anonymous/ ftp are the first things to try, with identical passwords.
Linux is supposedly the most stable and secure operating system and so inevitably most challenges want you to emulate the simplest hacks of the OS. So first we need to consider basic OS commands. Linux users will normally overload you with commands and switches and if you look into something like the ls command then you will find that it has many many switches, the vast majority of which are utterly pointless.
Passwd files. A lot of Unix/Linux challenges are about passwd files (/etc/passwd) which list usernames and encrypted passwords. The encryption is one-way and the OS checks your password when you log in by crypt(entered password)==stored password in passwd file ? The only way to get the original password back is to brute force guess it. To do that you will need John the Ripper or jtr as it is widely known. John is a sophisticated password guessing tool. In general you need to study this tool in depth to get the most out of it. Most challenge sites seem to think its a necessary attribute to be able to run jtr for hours on end. A good wordlist and a good set of rules will get you results, blind bruteforce will not and is generally a last resort. This file contains my preferred wordlist and rules. Jtr can also be used for other things, for example the KMd5 md5 hash cracker can be coupled to jtr to use stdin/stdout to run its wordlist and crack MD5 hashes.
I've linked to 'Hacking linux exposed' which is a good introduction to many subjects - user privileges, password cracking, linux files and structures, dns, tcp/ip etc etc.