Whatever you do, don't drop ship from China. You can buy things from China if you know what you're doing, but have them delivered from your house first. You're thinking about going into expert level right off the bat. Ebay isn't opposed to dropshipping, as I told them on the phone personally when they asked if I was (I called for a limit increase). They suggest a garbage (in their pocket) company "World Wide Brands" for dropshipping.
They are opposed to you sourcing cheap and counterfeit items, which is why if you sell tv's, smart phones, high end cameras, tablets, they'll likely pull your listing down since those are most likely to be fake.
Yes, you can dropship from Amazon, just make sure its from amazon or fulfilled by amazon because if they mess up the order you're stuck getting the bad feedback