This question is actually hard to answer, not because it is technically difficult, but for the lack of language precision that might be buried in it. I will answer it in two parts.
Raspberry Pi has a hand of different Linux distributions that can be ran on it, some are easier to install, some not so much. The "default" one, or at least the one that gets installed the most, is Raspbian, which is pretty simple to install and run.
You can find the files and the "supported" distros in the Downloads link. The NOOBS image is the easiest way to go, it will allow you to choose what you want in a interactive way. It has most of the Linux distros AND RISC OS, which isn't Linux. Nor UNIX.
But the issue here (and that's the language or concept lack of precision part) Linux is also NOT UNIX.
There are two UNIX-derivatives, which many consider real UNIX, that have working ports for the Raspberry Pi: NetBSD and FreeBSD. As a clarification, UNIX is a Copyright and needs permission to be used. As so, even these two aren't allowed to use the Copyrighted UNIX logo. You may also check NetBSD's statement about this which states the Copyright issue clearer, and check goldielock's answers and the comments at the end of this answer to decide that for yourself. Once upon a time, a real UNIX was considered something that shared UNIX code, inherited UNIX code or contributed to UNIX code. You can find the remains of that in FreeBSD's explanation.
I love them both, but not particularly for their easyness-to-install. I haven't tried the Raspberry Pi ports, but the regular PC-Intel ports are very hard to install for someone with little or no UNIX/hardware/partitioning knowledge.
You can check them out in their specific ports-page: NetBSD Raspberry Pi port and FreeBSD Raspberry Pi port.
If the person that assigned you the task is a UNIX-savvy teacher, you might go with the FreeBSD or NetBSD (which one you get installed first), because they might be considered closer to the historical UNIX. The Linux distros, RISC OS and Plan 9 are not. Else, just go with NOOBS and pick some of the readily available ones. I would go with Raspbian, but that's my personal preference.
And also, read goldilocks answer for another view on what is UNIX and what is not.