The right choice might depend on your user base.
If it mostly consists of private residential customers, it is likely that they will not need to make any difference between both addresses and that their main concern will be the shipping address.
If it is mainly made of business customers, things can be different for at least two reasons :
- the billing address is key for them to justify their purchase as a cost for their company
- the billing address is unique in many cases although the purchases sometimes need to be shipped to various physical addresses.
You should therefore go for the sequence that makes most sense to your user base and start with a concern that makes most sense to them. Your suggestion looks spot on if your customers are mainly residential.