In general, I don't think any particular care is taken in the packing of blanks, beyond ensuring they are inside a container. Garment decorators will typically be sticking them on the platen of a heat press and pre-pressing before doing a transfer or vinyl, or on the tacky platen of a screen press, either of which effectively deals with wrinkles.
That said, yours appear more wrinkled than average, so I don't wonder that you wonder about it
Assuming you are in the USA, that is indeed a long shipment time. Was something in the order on backorder?
I'm in Oregon, and typically get orders from CA or WA state in 2 days (that's at the Free Shipping price point, not paying for anything faster). On rare occasion the specific thing I need is in short supply, and I end up ordering from Florida, or the like--that takes a week.
When ordering there are typically options to state your preferences about how to handle items on backorder (wait to ship until everything is ready, or ship each thing as it becomes ready). From what you describe, I would guess that at least some of your items were out of stock and were shipped in separate packages as they became available. Also, drop-ship orders for third parties like blankstyle, might be a low priority for the manufacturer ... don't know.
I would set up accounts with some "real" wholesale distributors, as the pricing will be better. Most offer free shipping on orders of $200, a few start that at $150.
If you are in a state that has sales tax, you will need a resellers permit / license whatever they call it where you are, in order to buy from a real wholesaler. A few states, like Oregon, have no sales tax, and these places know that, but in that circumstance you'll look more legit if you have some sort of business entity setup (I have an LLC). I know in some states setting up that stuff can be a pain, but it's that or pay more for shirts.
I use my local distributor for everything I can, but for other things and for backup, I mainly use: S&S and Alpha Broder. Alpha can be a little confusing to use. Call and ask them to give you case pricing on pieces; it took me two tries to get that. They have a thing called Flex Shipping that costs $4.99. Rather than delivering to your door, FedEx drops it at a FedEx store of your choice (a great option if you have one within a reasonable distance). Note, in order to see this option at Checkout, you must have a credit card associated with your account.
Congratulations on your first big shipment. I had mine strewn all over the house as I inventoried it and sorted it away ;-)
