Keeping grass & weeds from growing in an area around my house?
"How can I keep anything from growing there?"
Several ways, depending on what your goal is. Is this "landscaping" in the traditional sense or do you just not want the grass to grow as close to the house, etc.? Permanent or how long?
Soil sterilant, usually intended for driveways, etc. will last six months to a year. You could mix that in a sprinkler can and put out a band just about the size of what you mentioned. Unless you would rather not use chemicals repeatedly.
Personally, I would go with the black plastic and mulch as already mentioned.
"I know I'll need to keep it edged."
A little more work up front, but if you will take a shovel and cut out a trench about three inches or so deep at the front edge before you put anything down, you will have a nice clean edge and whatever mulch you use will stay in the bed and not scatter onto the lawn area. In effect the front of the trench will serve as a retaining wall. Very little edging maintenance to do.
"Carefully spray once or twice a year to kill the wind-borne seeds."
Love me anyway but that is what they make pre-emergents for.
If it's worth doing, it's worth doing right. If you wouldn't put your name on it, it ain't done right!