There are thousands of people groups in the world (depending on how you “slice” the lists), and picking “one” can be very difficult.
The better approach (I think) is to pick a specific cluster. There are only ~250 clusters in the world, and most have a very well defined location, language, and culture. Then, work to reach the whole cluster.
Yes, there are cultural barriers between peoples within a specific cluster. That said, it’s often not that difficult to cross-culturally “help” the Gospel “over” those barriers–and very often, the people groups within the cluster can reach out to the other peoples within the cluster.
Of the 250 or so clusters in the world, about half are very unreached. Clusters are often named for the largest specific group within the cluster (e.g. the Uzbeks) but sometimes are made up of a number of small groups (i.e. the Atlantic-Wolof cluster, or the Urdu Muslim cluster–the latter includes some 377 specific people groups, making up about 100 million people).
Want a small but hard challenge–try the Nuristan cluster (86,000 but in a very hard to reach place). Want a larger cluster with some work presently going on? Try the Bengali cluster in Bangladesh, with 332 million people in it (> the population of the United States, 99% unreached).
So my advice: don’t struggle with picking out one people group out of 10,000. It’s a lot easier to focus on one people group out of 100. Check out the JP page on people group clusters.