that is called a interior french drain. locating the walls a few inches from the edge will work fine. there is a bit of controversey about vapor barriers. ours is stapled to the studs over the insulation. works fine. hopefully others will post links etc to various websites that discuss this. you can also google the topic too.

Consider using steel studs fastened to the walls, but stopping about 7" or 8" above the trough. Use studs deep enough to space the new wall surface out past the trough. Then cover the studs, leaving the space at the bottom open. Use a removable baseboard to provide access to the trough when-and-as needed. I have never seen nor done this- just something to stimulate your thought.