Hi,
I have been developing websites with Joomla since 2008. Lately I have handled a number of migrations from Joomla 1.5 to Joomla 3.2 I'm therefore skilled an qualified to deliver your project on time and budget. I also understand German which could make working on your sites easier.
I agree with your approach of not using automated tools as none of them actually works 100% so if you have little content it make more sense to migrate manually. I also makes more sense to take a modern responsive template as the basis of your new template and configure it to look like the old one, rather than try and transfer an old design.
In terms of content migration, as you suggest in your brief, configuring the menus and content first makes testing the template easier as there are already elements to display. So again I agree with your suggestion.
Once the Joomla 3.2 sites, populated with content are ready I would take over from you and work on both templates. I would use protostar, the free, standard, bootstrap based and responsive template that ships with Joomla 3. and tweak it to make it look like your sites with the addes benefit of being responsive for smartphones and tablets and using modern css markup.
Do not hesitate to contact me if you have any questions. I look forward to hearing from you and start working on you project.
Regards.
Xav.