Long Haul Upgrade Joomla 2.5 to latest and Hikashop 1.6 to latest

-- HikaShop version -- : 1.6.0
-- Joomla version -- : 2.5.28
-- PHP version -- : 5.5.30
-- Browser(s) name and version -- : All Browsers
-- Error-message(debug-mod must be tuned on) -- : none yet

Hi Folks

I am looking for advice as to how to go about the upgrade - and please don't say use the inline updates because these versions I have to upgrade from are far too old... I have tried on staging sites and no upgrades can seem to handle the big gap...

The web site has Joomla 2.5.28, PHP 5.5, Hikashop 1.6.0 Business (not my license, the charity I am doing the work for owns the license), Moodle 2.2... I think the starting point is going to have to be Hikashop upgrade, then Moodle, then PHP & Joomla as a final step... or it may be that I have to do manual updates on all sections all at once while the site is offline altogether...

So, my starter question is: What version of Hikashop can I upgrade to which will be compatible with PHP 7 and PHP 5.5 - that way I have a stepping stone to hobble to before Joomla update (which cannot go through as the server stands)

Regards