"The size is important to us."
Translation:Die Größe ist uns wichtig.
I am thinking that different expressions require different prepositions which are often not the same prepositions from one language to another and now that I see the above translation, that is probably the way to do it in German.
I too had tried "für uns" which was marked incorrect unless you switched to "bedeutend". We say that something is important to us or for us, but some expressions require something specific. Here it looks as though you could use either http://dictionary.reverso.net/english-german/Important%20to%20us Perhaps it is more common to use "für" with "bedeutend".
"nach" is just not the right preposition for this. In English "to" is just used for so many different German prepositions. "nach" can mean "after", especially with time rather than "to". http://dictionary.reverso.net/german-english/nach http://dictionary.reverso.net/english-german/to http://dictionary.reverso.net/german-english/bedeutend
The conjugated verb is usually in second position. Think of the sentence "He threw us the ball." which means that "He threw the ball to us." German may prefer the first sentence. The indirect object is used with more verbs than in English. We would not say "The size is us important." instead we would have to say "The size is important to us." or "The size is important for us."