You do not lose any rights by publishing on Medium, other than the right to call the poems "unpublished." Which matters only to those editors and publishers who have a policy of only considering work that has not been published previously elsewhere. You can definitely self-publish your collection--whether through Amazon or Lulu.com or your nearest photocopier--but be aware that few bookstores will carry self-published books.

You can also submit a collection (including previously published work) to a traditional publisher or enter it in one of the many contests you will find at newpages.com, most of which have nice cash prizes. The downsides of the contests are (1) the entry fees, and (2) the competition, which normally includes many professional writers. The upside is that your work, if selected, will be improved by professional editing and gain access to commercial markets. Plus, of course, the prize and the prestige.