Is VAT payable on goods sourced in China and drop-shipped directly to the customer by the vendor?

Question

I am setting up an ecommerce business selling products online which are sourced in China and sold to customers who are both UK and non-UK based. Please can you advise if I should be charging VAT on these products and/or on the shipping? Some of the offers will be ‘retail price with free shipping’ and others will be ‘free, just pay for shipping and handling’. Many thanks.