There are several free ePub creation apps. You could self publish a chapbook and display it in iBooks.
Alternately you could create a PDF book or document. This would give you better control over the layout. There are numerous PDF readers, including iBooks that would let you show them to advantage. Even if you saved each poem as an individual PDF file you could select and display them from numerous apps. GoodReader being a well organized choice that would let you save the files in a folder structure.
I would prefer to do that kind of work on a computer. But if you wanted to you can produce a decent layout using Pages. Those files will export as PDF for display in other apps, or you could just leave them in Pages. I don't recommend that though. With as many poems as you are suggesting, keeping individual files for each poem would get cluttered, and putting them all in one document would be give you the same problems as using a note taking program.
If you plan on always having access to the internet you could break your files down to individual poems, text or PDF and save them in DropBox. Again you would be able to keep them in a file structure. More importantly you would have access to them from multiple apps, on multiple devices, anywhere you have an internet connection.
Ok, it occurs to me that this question is too broad. I could go on with options forever. but maybe I've given you some ideas.