I haven't read poety on my e-reader, but I would most definitely not switch to landscape mode to do so.
Re stories: Generally, if I buy an anthology, it's because it includes particular authors and/or titles I want to read. So I'll turn to those first. Then I might skip around based on whether I've heard of an author, whether a title appeals to me, even how long the story is. Rarely would I read straight through.