EDIT: Sumerian. Thanks kookingpot.
This could be personal records or poetry (i.e. Gilgamesh e.t.c). Similar to how ancient texts like The Odyssey is set out in some versions. I would like to compare the symbols with the translation. (Phonetic is a bonus!)
The older the better. I'm looking for c. 3000 BCE as a sort of example of the first evidence of written 'human nature', whether it be letters to friends or works of fiction. I am trying to avoid administrative texts.
I can't seem to find any, but maybe I'm googling the wrong keywords.
Which cuneiform language are you looking for? "Cuneiform" is a writing system, not a language, and several Ancient Near Eastern languages used cuneiform writing systems (around 15 different languages overall), and so your comparisons will differ depending on which language you're looking at. Are you looking for Sumerian, Akkadian, Ugaritic, Elamite, Old Persian, Hittite? 3000 BC is going to be pretty much exclusively administrative stuff.
If you're looking for Sumerian literature, start here. It'd hard to find non-administrative texts before the Ur III period. When you find a text, you can look at the bibliographies of the works which should have images of the texts, transliterations, and translations.
Here (PDF warning) is a book that lists a bunch of Sumerian texts (most Sumerian texts are administrative/economic in nature) and provides pictures and translations.
/u/kookingpot is correct about 3000 BC being pretty much comprised of administrative documents. Cuneiform signs are not legible at all to the untrained eye, so I am not sure how helpful it would be to have a side-by-side document with signs and a translation for you. For example, look at this image of an excerpt of the law codes of Hammurabi.
Otherwise, ETCSL, which /u/kookingpot references, is a good place to start for scholarly editions of Sumerian texts. Sometimes, the CDLI database has images and editions of cuneiform tablets, such as with this text. But you have to know what you're looking for in advance. It is unwieldy to try and browse on your own.