Best way to update from 2.3.0 to 3.2.1?

Hi,

There is better.
Export the hikashop tables in your phpmyadmin, change the table prefix in the file, delete/rename the tables you already have for HikaShop on your new website, import the file in your new website and install the latest version of HikaShop. It will add all the missing columns and tables and it should then work fine. You'll get back all the products, all the orders, etc etc.
If you have user accounts for the orders, you'll want to set the user_cms_id to 0 on all the entries in the hikashop_user table so that all the previous orders are considered as guest purchases and that there won't be a mismatch between the ids of the user accounts in joomla and the entries in HikaShop.