As a non-EU based online retailer, a key consideration would be to decide whether or not you will be the ‘Importer of Record’ - this determines who will be responsible for the import charges.
It could be in your best interest to VAT register in the country where your goods are imported since your customer will not be responsible for all import charges and logistics relating to his purchase. Most non-EU retailers experience considerable return rates when the customer cannot complete the import themselves.
An EORI number is unique throughout the EU, assigned by a customs authority in a member state to businesses. By registering for customs purposes in one member state, an Economic Operator is able to obtain an EORI number which is valid throughout the EU. The EO will then use this number in all communications with any EU customs authorities where a customs identifier is required for example customs declarations. Having an EORI is necessary in order to clear goods through customs in the EU