Hi,
Custom address fields, that you can create in the Starter edition are displayed with the address creation/edition form.
So you see them when you see the registration form.
So with the Starter edition, since you can't have guest checkout, the first time you checkout, you register and thus you see these address fields. And the second time, since you already entered your address, you login and you already have your previously entered address with these fields filled.
Moving to the Essential edition will solve your situation since you'll be able to configure HikaShop to work with only the guest checkout, and thus each time you checkout, you'll have the email and address fields to fill.
Doing so with custom coding with the Starter edition will be complex. Since you plan to go with the Essential edition anyways, I would recommend you move to it and then configure the checkout like you need and it should work like you want.
Custom order fields, available only with the Business edition, are more suited to your need as you they are linked to the order itself and thus display on the checkout regardless of whether you're doing a guest checkout, or a registration or a returning order.