To sell on amazon.com, you need a UPC code, not a bar code system.
What's the difference? A UPC code is just a unique number given to you buy a business licensed to do so (much like domain name registrars actually). They give you this unique number, and an image of the actual bar code if you wish to use it. Each individual retailer (such as amazon) then links the UPC number to your product in their system.
I was in a similiar system. I got the UPC code for an inexpensive price and put my products on amazon.com. I am glad I did so, because it not only gives you an additional market to sell on (people who might not have otherwise found your product), but also gives your product legitimacy when it is googled and it's amazon.com page comes up on the search results page.
The UPC/EAN code and barcode are treated as synonyms as the latter is just a physical representation of the former.
You will need a company code assigned by GS1 in order to use Amazon but if you are doing your own fulfillment physical barcoding would not be necessary. If somebody else handles your fulfillment or if you supply a reseller then barcodes will be expected.