Vendors are able to reject orders. A good example is if you don't encrypt your shipping info, the order may be rejected. The 'new' status means that you have sent the order, but the vendor hasn't accepted it yet. The next statuses are 'accepted', 'shipped' and 'finalized' or something along those lines.
Don't tell the public where you've sent xmr from. But now that you've sent the funds, wait for the Vendor to Accept. Once accepted, it should be shipped shortly.
The "New" status means that your order has been made, but not accepted or shipped by vendor yet, you don't need to do anything else.
The "Accepted" status means the vendor is working on your order but hasn't shipped it yet, and the "Shipped" status means that the order has left the vendor and is now in the hands of the postal service.
Once your order arrives and you make sure you got what you paid for, finalize the order. Leave a review if you feel like it.
The order status will be "finalized" when you finalize it(release the money to the vendor) and the status will be "done" if you leave a review.
The "Cancelled" status shows when the order is cancelled by you, rejected by the vendor, or refunded in the case that something goes wrong.
To answer your question - New means your money has been received and is waiting for the vendor
Next is accepted - the vendor can read your PGP information, is in stock, has no questions
Shipped - the vendor has marked this shipped and the auto finalization timer starts. Make note of the date. Extend 1-2 days before if necessary. Finalize once you receive product and are satisfied within 48 hours (Don't take a week to test the product if you use it on weekends, use reagents, etc.)