The Doc is one of my absolute favorite characters in Voyager, and perhaps all of Star Trek.
I think he kinda reminds me, in some ways, of Major Winchester from M*A*S*H*, and of Dr. McKay from StarGate Atlantis. All three could be real blow-hards, but when the situation demanded it, their ethics were second to none, and they did the right thing, even if it meant bending a rule, or taking firm measures to do so.
The Doctor, to me, is a melding of Leonard McCoy, and Commander Data. On the McCoy side of things, he always had that "I'm a doctor, not a (insert needed function here)", and a sometimes irascible wit....and other times, his sarcasm and sardonicism could shine through with class. On the Data side of things, the Doctor sought acceptance among the Voyager crew the way Data did amongst his crew, and amongst humanity itself. The Doctor sought to better himself by studying humanity, and even by being a coach in humanity as he became the mentor for both Seven of Nine, and before her, Kes. (Although Kes was a much more easy going pupil.
It is a credit to Robert Picardo that he made the Doctor so relatable. He straddled an emotional tightrope at all times, never being too overjoyed or too angry or too upset....always striking just the right balance to let folks know how he felt without needing to go full on with whatever emotion he felt at the time.
One of my favorite episodes is the one where the Doctor experimented with having a family. The family first started out being like a 1950's "Leave It To Beaver" type family...or perhaps a bit more extremely, almost Stepford-like-ish-esque. And then, when B'elanna monkeyed a little bit with his simulation, the family became dysfunctional. The tragedy of his holo-daughter always puts a lump in my throat, the scenes were so beautifully played.