I find this depends on what you mean by 'highly readable.' Some people want the classics that flow easily, others want contemporary stuff that feels like a conversation. I stumbled on the Poetry Foundation site ages ago when I was trying to remember a line from Emily Dickinson. Their collection is massive and the site's actually pleasant to browse, which is rare for free literary archives. You can filter by subject, occasion, even poetic form, which is handy if you're looking for sonnets or haiku that don't feel like a chore to parse.
For newer poets, I keep going back to Button Poetry on YouTube. It's not a text collection, but seeing and hearing the performance adds a whole layer of accessibility. The poems are often about modern life, identity, politics—stuff that grabs you immediately. Reading the text afterward feels different, more alive. I've found poets there I never would have in an anthology, like Rudy Francisco. His work just... lands.
Honestly, sometimes a good old-fashioned library app is the simplest path. Libby, connected to your local library card, usually has curated poetry collections and sometimes even contemporary ebooks. The 'readability' comes from someone having already done the selection work, pulling together themed compilations like 'Best American Poetry' annuals. It's less about digging through a database and more about stumbling onto a complete book that's already vetted for a general audience.