I'd suggest Good Poems by Garrison Keillor. http://www.amazon.com/Good-Poems-Garrison-Keillor/dp/0142003441
It is a collection of the most popular poems that he read on public radio's Writers Almanac in the morning. There is a wide range of types of poems and poets, but all have been "radio tested" as he discusses in the introduction to the collection. It's a great place to start.