How do I write non-rhyming songs? and how do I add guitar to it?

I have a very easy time writing rhyming songs. But I don't if it's just me but it seems that some bands have a couple rhyming songs and a couple non. I don't know where to beggin with a non-rhyming song though. I can pretty much write the lyrics but when it comes to writing the guitar chords for it.. it's very hard.. How do I find the chords that sound good? And how can I choose a couple chords and finger pick them and make it sound good. Like the song Let It Die - Foo Fighters.. It's the same chords being picked again and again and it sounds good with the singing. Also since I'm used to writing rhyming songs, they're going to be the main ones I write.. But if I write about 10 songs what would be a good ratio of rhyming and non-rhyming songs?