The first actual rule in the fifth edition DMG:
The D&D rules help you and the other players have a good time, but the rules aren't in charge. You're the DM, and you are in charge of the game. That said, your goal isn't to slaughter the adventurers but to create a campaign world that revolves around their actions and decisions, and to keep your players coming back for more! If you're lucky, the events of your campaign will echo in the memories of your players long after the final game session is concluded."
This, in one form or another, has always been the first and primary rule in all editions of the game.
There is a sourcebook from the second edition that you might want to check out - The Complete Book of Necromancers. In that book, they show how you can be a good necromancer - essentially a necromancer is first and foremost a specialist in the School of Necromancy. Most healing spells are from that school, and versions of clerical spells could easily be researched.
Now, as for the animate dead issue, remember that the Negative Material Plane is not itself evil, just like the Positive Material Plane is not good (it is the source for healing magic). Now, in my campaigns, I allow animation of neutrally aligned undead to do tasks such as building, digging, and other very simple labor tasks without it being evil, as long as the necromancer puts the undead back in their graves at the end. There are many precedents for this in fantasy fiction (see the Xanth series). I see mindless undead as soulless, and therefore you are not necessarily doing an evil act.
There is an interesting part of the 2nd Edition Van Richten's Guide to Vampires. They discuss whether or not a vampire can be good-aligned. It concludes that they can at the beginning, but, as time goes on, they get bitter and their alignment slowly shifts towards evil and chaos. It can take a couple of generations, but it happens.
Look at the reasons that a particular form of the undead that is created. If it is for selfish reasons (such as the lich), or due to evil choices (such as the death knight), then their creation is evil. They retain their souls but raising one who a soulless is a neutral act. BTW the mummy has been postulated to be connected to the Positive Material Plane (Von Richtens's Guide to Mummies).
Mike Hinshaw