Actually red oak is a hardwood, but it is not the greatest for outdoors. Redwood would be a good choice, as well as western red cedar, both of which should be available in your neck of the woods, though they are fairly soft. For a hardwood, white oak is a good outdoor wood and plenty hard.
The big box stores are far from the best places to buy hardwoods, prices way high and choices extemely limited. Search out hardwood dealer in your area and he'll have much better choices. You might also be able to find someone with a band mill who cuts local woods and they generally offer some better bargains.
Red Oak has virtually no resistance to decay, so in my view, it's a very poor choice for an exterior application. I don't have any data on Poplars durability for exterior usage, other than it is a very stable wood once it has reached eqilibrium, probably why it's desireable for millwork that's to be painted...
Hardwoods that would be "desireable" for your use would be White Oak, the Mahoganies (Phillipine, Honduran), Locust, Ipe, Mesquite, Ash, and Teak.
Softwoods would include Western Red Cedar, Redwood, Port Orford Cedar, Southern Yellow Pine, most Spruces, and Baldcypress...FWIW.
Teak is a perfect wood for outdoors in my opinion, so is Mahogany, though both will run you a bit more. Cedar wears well and age's outside to a grey color if left untreated, but it too is nice, less expensive and light weight for doors, though not as strong as the others.
The most rot resistant woods in our area of Western NY include locust and white oak. Poplar, while not considered rot resistant will last many years without a finish and many more years with a finish. If redwood is too soft for you, poplar will also be too soft. www.garresonlumber.com sells both select locust and white oak for around $2.50/BF, way cheaper than home depot even with the shipping unless you live closer to the West Coast.
Sawduster, it seems like you know a lot about buying wood. How does one go about finding good lumber in their area? My town has a lowes and fleet farm, both of which sell wood. We also have a 'lumber yard' which is generally way more expensive for the same lumber. But - do you think a place like this would have stocks of pre-cut plywood 2 feet by 6 feet? Or possibly 2 feet by 8 feet? The standard 2ft x 4ft stock seems inadequate for some applications for me, yet I hate cutting large stocks of wood down.