[quote=@Gisk]
So we need to know those three spells before we can learn any other magic, but are there other prerequisites?  Do we have to learn magic in a "chain" of progressively stronger magic?  Or can we learn any(basic leveled) spell after learning those three?
[/quote]

any base level magic can be learned after the initial 3. 

so reflect, gravity, magnet, those all work.

Super strong spells that don't have a family, like Holy.... those should be reserved for later.