I am not an expert on where to submit short stories, poetry, and manuscripts. But I have developed a word document listing where I have sent work, so that I can be sure not to send too much too often or send the same materials either to the same publication at different times or to two publications simultaneously (something many publications don’t welcome). A brief biography is often needed, and I have developed another document for a quick copy of my merits.
There are many places to send work. It seems a little more than half charge a reading fee, especially for contests. Poets & Writers publishes a compilation of where one can send materials, Google searches will bring up its slew of results, and Submittable, which is used by nearly every publication as a submission portal, provides a list of what publications have open calls. I have used all of these methods, there are undoubtedly more, to find and submit poems and short stories. I have so far limited my search to free submissions, and there are many opportunities. A Submittable account is free to set up, and I would recommend it as the best way to get started in trying to publish work.