Pretty sure the students are taught by the younger graduates. As they age they realise that instead of doing complicated research that probably won't impact their own lives they could just sit tight with their old pals, safe in the knowledge that they've been doing magic for so long that nobody will try a damn thing.
Generally among the community: Death is the most popular character. After that it's a close Vimes. When you're writing about or from the perspective of any character, including these two, don't focus on their magical abilities. Focus on who they are, not what. Death struggles with being forever an outsider, he tries so hard to understand humans but can never seem to quite get the point. Vimes (minor spoiler) has a demon living in his fore-arm. But what we find interesting about Vimes is his constant long for the chase, his dedication to his son and his job, and his struggle with what he calls The Beast (Monstrous Regiment for that specific metaphor, but it's a common theme).
Characters like Rincewind and Lu-Tze provide us with respite, but the ones we really care about are the deep and nuanced leads with long-lasting struggles that have forged multiple books single-handedly
Monstrous Regiment is a good shout, might also be Thud! as that's the one where Vetinari is trying to make him hire a black ribbon constable?
Either continue through the City Watch series (Men at Arms), give the Witches a shot (Equal Rites), take a look at Death (Mort), or read his greatest one-shot Small Gods. I'd say it's best to read each mini series in full rather than jumping about your first time round, but if Vimes doesn't really click with you as a character I'm sure either Death or Granny will :)