I don't even see why anyone even bothers with necromancy. Why not just summon Daedra? They're a good deal smarter, and better than just a meat shield, and I say that because there can scarcely be any any use for dead servants beyond that. Lichdom works, but aren't there better ways to immortality besides turning yourself into a hunk of rotting flesh? But I suppose we don't have much of an example of useful necromancy yet in the games. They existed solely as villains in Oblivion who didn't have anything to do but hang around in old forts with their creations.
Though never really seen to happen, only spoken word of mouth, inexperienced mages do have issues with daedra breaking their control, and bashing their former master to death or wrecking the place up. It really does take a good deal of effort to summon, let alone control a daedra.
In addition, daedra have the issue of not being able to remain indefinite. While a mage can use loopholes to get a daedra though summoning, eventually the daedra is forced back. The only real way to keep it bound to Mundus, is if you are either Vivec, or bind it to something (I forgot the actually process, but there is a book that explains it, and it also involves the daedra willing to go though the process).
With the undead, they tend to last indefinitely, or until their master is killed. In addition, multiple can be summoned and kept indefinitely. The undead don't really seem to have many, if any, issues with suddenly attacking their master, which is a big plus. However, it should be noted undead beasts have been known to attack inexperienced necromancers, and work at best as a guard dog. Humanoid undead tend to be preferred, due to being able to complete more complicated tasks, while remaining mindless and obedient.
As to why someone would want to become a lich? Depends on the person. Necromancers that chose to become liches tend to be really powerful wizards already, and usually do it to extend their life to become immortal. This way, they can continue their research, practice their magic capabilities and become more powerful, protect dangerous and powerful artifacts from getting into anyone's hands (as seen in Tribunal), or other reasons. You don't have to be evil or completely immoral or amoral to be a lich, though a lot of liches tend to be in the amoral category. An example would be that one undead guy in Bloodmoon, who, even though exiled from the Skaal but still, tried to warn them of an impending attack from daedra. Even though he was still an outcast and generally disliked, he still contained the daedra, and turned himself into a lich so he could continue holding the barrier as he become too old and frail.
http://www.imperial-library.info/mwbooks/corpse_preparation.shtml is a really good source for most of your necromatic needs