Actually, you don't want China. You want somewhere like South Korea. But you can still find the stuff in China, where most of what SK makes goes to.
Unfortunately, you aren't going to find shirts that are "sellable" for $1-$4. At $5 you are just starting to get into clothes that you can actually sell to people like westerners, who are typically the ones willing to spend $20 for a shirt online. When I say "sellable" - this is in regards to style. You just aren't going to find good quality clothing for a really cheap price, unless you are planning on dropping a couple thousand dollars on an order of shirts. Or you can be Walmart and strong arm suppliers/manufacturers into selling shirts for $1, but even then, they are purchasing 100,000 shirts.
Also, something to keep in mind, Asian manufacturers don't typically manufacture clothing in sizes designed for non-Asians. A XL in China will be like a M on the average westerner, and short clothing is a common problem. Pants not touching the ankles, shirts stopping at the belly button, etc. Also, in the west, a low quality shirt could last a while, in China, a low quality inexpensive shirt might be lucky to last a couple washes.
A $3 shirt looks like this:
A $6 shirt looks like this:
If you know anything about the retail clothing industry, you are going to aim for a starting 350% mark up, which means that you will have to sell the first one for $10.50, and the second one for $21. Does that seem reasonable? And then once it doesn't sell after 3-6 months, you want to rotate your stock by trying to sell it for at least 200% to pretty much get rid of it and still cover online fees, which means you are selling that first one for $6, and that second one for $12. These prices probably look pretty similar for these unbranded styles you find at Malls in the U.S. Never underestimate the marketing and the cost of that marketing behind some of the name brands we all know.