Learn Finnish: Sinä tahdot aina enemmän.

Both verbs mean "to want." Tahtoa is often slightly stronger and implies willpower or determination, whereas haluta is the standard, most common word. In many contexts they are interchangeable, but tahtoa gives the sentence a slightly more demanding feel.

Is enemmän related to a specific base word?

Yes, it is the comparative form of paljon (a lot / much). While regular comparative adjectives end in -mpi, the adverb for "more" takes this special form enemmän.

If I wanted to say "You always want more money", what case would the word for money take?

It would take the partitive case: Sinä tahdot aina enemmän rahaa. When enemmän expresses a quantity of something, the noun that follows it must be in the partitive.

Why is aina placed after the verb rather than before it?

In Finnish, adverbs of frequency like aina (always) most naturally go right after the verb in a neutral sentence. Saying Sinä aina tahdot enemmän is understandable but sounds heavily influenced by English word order.