Hi,
First, you should ineed move the Joomla users. There are many tools for that on the JED. I'm not familiar with them so I wouldn't be able to recommend one over another.
Then, you should download via FTP the files/folders in images/com_hikashop/upload and in media/com_hikashop/upload/safe (or the other paths you set under the Files section of the HikaShop configuration.
Then, upload them in the same folders on the new website.
Then, in PHPMyAdmin, you can export all the tables with hikashop and hikamarket in them.
Then, in the export file, change the table prefix if necessary with a search and replace (for example with notepad++).
Then, in the new PHPMyAdmin, you can import the file to get all the tables of HikaShop from the olad website in the new.
Then, install HikaShop on the new website and you should get back all your data in HikaShop. You'll just have to reconfigure the modules, plugins and menu items since their settings are in Joomla tables, not HikaShop's.