The 'Conjuration - Reanimate' spells you can get improve as you level up your Conjuration Skill:
(Conjuration - Reanimate Spell, Conjuration skill level requirement, and the spell description)
Raise Zombie - 0 - Reanimate a weak dead body to fight for you for 60 seconds
Reanimate Corpse - 25 - Reanimate a more powerful dead body to fight for you for 60 seconds
Revenant - 50 - Reanimate a powerful dead body to fight for you for 60 seconds
Dread Zombie - 75 - Reanimate a very powerful dead body to fight for you for 60 seconds
Dead Thrall - 100 - Reanimate a dead body permanently to fight for you
Based on these descriptions, it is hard to know what exactly the spell will work on. What is a weak dead body? A more powerful dead body? A powerful dead body? etc.?
Skyrim classifies creatures and NPCs into generic classes as enumerated on the pages below:
Within each of these classes, there is also a breakdown of more powerful types of those classes that are added as the player levels. So within the Bandit class, there is the initial Bandit, then the Bandit Outlaw, then the Bandit Thug, etc. From this information, it seems apparent that the weak, more powerful, and powerful descriptions may be related to the type within each creature or NPC class as the types themselves do not scale to the player's level with the exception of boss-types. The Reanimate spells' qualifications of power may relate to class as well.
...all leveled enemies are generated more like leveled creatures in Fallout. For example, Bandit NPCs are always a fixed level for their name (Bandits are level 1, Bandit Thugs are level 9, Bandit Highwaymen are level 14, etc). The player's level affects the range of possible bandit types generated within a bandit dungeon, and probably the frequency, but does not seem to affect the resulting stats except in a few rare cases. Lower variant bandits remain reasonably common even when more dangerous bandits are available.
To optimize magicka consumption, it would be useful to know the minimum level of reanimation spell necessary for a given class and type of enemy. So, what is the minimum level of reanimation spell needed for each type of each creature and NPC class? It would be nice if there were a set of general rules such as "regardless of class of creature or NPC, if they appear after the player is between levels X and Y, then you need at least the level Z conjuration spell" or "these classes of NPCs and creatures all need at least the level Z conjuration spell."