The complete mitochondrial genome of thousands of humans, a few Neanderthals, Denisova man, dozens of chimpanzees, a few gorillas, orangutan, etc. have been sequenced. The past few years there have been a lot of popular press stories, books, and scientific papers about what all this data can tell us. Did pre-humans mate with chimpanzees? Did prehistoric Europeans mate with Neanderthals? Etc. It’s all quite interesting, and there is fossil and/or archeological data to go with the DNA data.
I don’t think most of the questions are the type that students can answer with a few genomes sampled from the thousands done. But there are dozens of very good questions they can answer, such as: Do trees built from the COI gene give the same answer as trees built from complete mitochondrial genomes of the same samples (maybe 3 humans, one Neanderthal, 3 Chimpanzee, 2 gorilla and one orangutan genomes in the data set to be analyzed)?
If you pick a 100-base long region at random, is the tree good? What about a 500 base region? What happens if you use macaque or baboon as the outgroup instead of orangutan? Do maximum likelihood and neighbor-joining methods give similar or identical results? Does selecting the model of evolution (Kimura, F84, GTR; with or without a gamma distribution) make a large difference? If we use 8 million years as the date of the common ancestor between chimpanzee and human, when did Neanderthal share a common ancestor with human?
I can think of thousands of great HIV data sets, but like Trypanosomes or fruit flies or most other organisms, the students are unlikely to understand how the organisms evolved and so are unlikely to be able to asses when the data support or refute various ideas about the evolution based on other factors such as phenotypes.