If they seem like good people, just go over some afternoon and ring their doorbell. Or next time you see them outside washing their car or gardening or something, stop by and tell them exactly what you want to do. I think that'* the best way to handle it.
However, we had some real ******* neighbors and between our yards was an unsightly fence that was on their property. It made that side of our lawn look like crap and my old man got sick of it. So we put up a new fence on our side (only about 6 inches from theirs) and waited for them to take the hint. My dad tried telling him what he was gunna do but the guy was a real dick so we just went ahead with our plans. But if at all possible just do situation #1. I'm sure they wouldn't mind a brand new fence at your expense. Ask if they have any requests as far as size/color/style. After all, they do have to look at it too.
2001 Grand Prix GTP Special Edition
1997 Bonneville SLE- Totalled
August 2004-March 2007