Chain link fence is sort of the default for dog fencing. If you decide to go this route, I'd spend the extra money and get the steel cable that gets laced through the bottom row of holes and stretched tight. This is prevent any "fence testers" from pushing under the fence.
I helped a friend of mine with some fencing around his garden this past weekend. He used Cattle Panels (http://www.tractorsupply.com/feedlot-pa ... t--3502077
). They're probably not quite as cheap as chain-link, but they look better IMO. They're also A LOT EASIER to work with than chain link. If you're going to have young pups around, I'd get the panels with smaller openings. He used the panels with 4"x4" openings, and I think a small pup could squeeze through.
Good luck. Bad neighbors are a problem that doesn't go away easily.