That's a toughie! Normally, I'd put cedar, poplar or bamboo, but the septic system makes that problematic - at least. Anything that grows tall will have deep roots.
Have you considered climbing plants? Of course they need support, so you'd have to build a frame. It looks like a long stretch and would be a lot of work, as well as expense (which is likely a consideration when you've just bought a house.) For a cheap, quick fix, you might think about Pampas grass - but y6ou'd also better think, right from the start, about how to contain it.
