Well, there's a chance that a few of them would actually sell. I've sold some low level rares with unusually high stats before... but the amounts they sell for on the AH just aren't high enough to justify it. If you can spot a few rares that have really high main stats, those are the ones you'd try to sell. But generally I don't think it's worth it.
I'd just vendor them and save all my gold until around level 50 for a high DPS 2H to make Hell really easy. I wouldn't really try to sell anything on the AH until you get to Inferno. Possibly late Hell... but I wouldn't care enough to do it.
What stats are the most popular on the AH and what items are the most rare (shoulders, bracers, rings, amulets...)?
well all items are rare and the stats that are most popular depends on classes, for example im a barb so i value a lot on crit, vitality, all resisit, and strength. If you find a armor or shield that has all that, all the barbs will buy it from you and you should compare that item with other items in AH with the same stats. Once you have compared undercut the item by 20-30 percent.
It's kind of hard to say, because many of the stats/affixes depend on what else is on the item, and what class is looking to buy the item. For example, +Armor can be great, but without other good stuff it's probably not going to sell. Or, people love buying high primary stat with good VIT, but high VIT by itself typically won't sell, and high primary stat by itself does at least have a (small) chance to sell. Again, it's hard to explain all of the different exceptions by item type, what's on the item, and what class it's for, but there are some stats that do stand out.
Increased Attack Speed
Critical Hit Chance
Critical Hit Damage
Max Slots (3 for Chest, 2 for Legs, 1 for Head, Amulet, Ring, Weapon, Off-Hand/Shield)
Primary Stats (DEX seems to still sell the best/for the highest prices)
And then these are pretty decent if coupled with the above:
Life on Hit (mainly on weapons around 600 or higher, but if really high on amulets/rings that's good too)
Magic Find (this is probably going to be more sought after very soon so I figured I would include it)
Movement Speed (mainly just on boots, and only if it's in addition to the above stats)
Basically, the more of these you find together on an item, the better. As for "what items are the most rare," I'm thinking you mean which ones do people want the most to find with good stuff on them? That would be (as far as I know) Amulets and Rings above all else, then Gloves, then Helms, and maybe even Bracers at the end (sure why not, lol.) I believe the reasons for this are:
Amulet and Rings are the hardest items to find with great stats on them (making them the most expensive items in the AH)
Amulets, Rings, and Gloves can roll IAS, Crit Chance, AND Crit Damage on them ("trifecta")
Helms and Bracers can roll Crit Chance, but Helms can also roll a socket which can be very useful
So yeah, hope that helps, and if anyone sees this and thinks I've got something wrong, feel free to correct me.