Choosing a quick and easy mesechta of mishnayos is a highly subjective activity.
The first consideration, obviously, is length. However, there are plenty of relatively short mesechtos, so this is not a major problem.
The biggest issue, especially for someone with a limited background, is to avoid having too many new concepts at once, especially big complicated concepts (such as inyanei kodshim and taharos).
My personal recommendations would be either Megilah or Makkos.
Megilah is a well known "easy" mesechta.It is only four chapters long and most of the topics covered (e.g. Purim, krias haTorah) will already be basically familiar even to a relative beginner.
Makkos is, admittedly, a less obvious choice. While only three chapters long, the topics covered (false witnesses, exile for unintentional murder, and the penalty of lashes) deal with criminal law, and will not be immediately familiar to a beginning student. However, the key concepts of each chapter can be presented fairly quickly, and once grasped, the details of each chapter are fairly straightforward.
In my experience, having taught both of these mesechtos, brighter students generally found Makkos to be more interesting and stimulating than Megilla. However, as I said before, this is a highly subjective choice.