When constructing a language it is tempting to include every possible noun case. Don't do this. Not even once. I'm not trying to "crush" anyone's "creativity" but German has four (Nominative, Accusative, Dative and Genetive) and hardly uses all of them. Genetive is used rarely in conversation while the Dative probably wouldn't be used at all were it not for prepositions that required it. Still each case does serve a function so too should any cases that you use. That said many languages have ways to change a noun's case with prepositions. You could, as a feature of your language have pronouns in a case that normal nouns don't normally have. An example in English is "Whom" - this is left over from a dative version of "Who" popular in Germanic languages. Furthermroe you may have cases which share noun forms, such as a combined instrumental and locative form which could be determined only by context though could be cleared up with another word to indicate direction shouldformal writing reguire all the details.
Nominative case tends to be the default case for a noun, I can not honestly think of a language which does not use nominative case even if the form is shared. All sentences in all languages have a subject or actor.
The accusative case for direct objects is common in languages which make use of a case system. It may not be needed if you have a very strict word order or other strict grammar rules which will make your direct object clear. Or if you're making a tedious language where all verbs are intransative (please do not do this I will hit you in the head with a newspaper lord so help me...)
The Dative case, for your indirect obejcts. Stypically Accusative and Dative objects do not share a form but Nominative and Dative could. No matter how strict your word order for subjects verbs and direct objects may be your indirect object may or may not be linked in though some kind of preposition but prepositions can also come before direct objects in many languages and sometimes even the subject. The advantage of the dative is that if it marked seperate from the accusative you know right away which is which.
Genitive case is an object which is owned. Many languages simply use a posessive noun or pronoun which often functions similar to an adjective to show an object is owned. It seems that the owner is usually relevant enough that you're mentioning him or her anyway. Other languages, such as Spanish use an x of y pattern which does get some use in English as well. Even languages which have a Genitive case usually do not use it with a posessive noun. As much as this seems useful you could probably give this one a miss.
There are other fun cases such as locative and instrumental and you can use them to omit some prepositions or other bits of grammar if you want to have as few words as possible. You could possibly have genitive and locative share a form, likely the verb would omit any ambiguity-- I can not come up with an example that would be contextually unclear but maybe you can.
I kept this short because it is just my current thoughts on the subject. I will update this page as I think more and my thoughts and feelings change.