How certain are you that your supplier will do everything right? Are you willing to bet your entire future of selling on Amazon on them not doing it wrong; possibly by shipping sub-standard product?

If you are not 100% sure, then at least for the first shipment, you should have it sent to you, so that you can verify that it's what you think it is, and also can properly prep the items for FBA. Note that one shipment of counterfeit or substandard items could be enough to get you banned from Amazon for life.

As for labels, there are two labels you need to be worried about. First is the FNSKU, which is applied to each unit you are selling. This is a barcode that identifies not only the item, but you as the seller. It is not a shipping label.

You will also need a shipping label to go on the box(es) you are shipping to Amazon. This is a UPS or similar label, along with an Amazon specific label, that you can print out.

Any printer can print labels; just make sure you buy the labels suitable for your printer (laser, inkjet, or thermal).

If you decide to have your supplier prep everything for you, you will need to work directly with them to figure out what you need to provide.

I hope that you have gone through Seller U, and understand proper sourcing of items. Read through the forums, pay special attention to the threads with titles such as "IP violation" or "I've been suspended" or anything mentioning "Section 3". If you don't have the proper permissions to sell your items on Amazon, then labels may be the least of your worries.