The stone you're showing, while one can make a path out of it, is not really the best path material. A stone that includes all particle sizes down to sand & dust packs to a better walking surface. While it drains, it doesn't suck water in like a sieve, as does the stone comprised of one particle size (as above.) You would need to grade walk to drain and could abut house if you use proper material. This presumes you don't already have foundation problems with water infiltration.