Does it make a difference as to x68 or x86 based architecture?
>>> '''I'd love so much to have a nice custom and "special" harware where to run my beloved Amiga OS (and the Amiga was and is a great mixture and cooperation between software and hardware)'''
Yes, I agree Onix.
The term 'home computing' nowadys, seems to be now PC or a Mac, which are used in office and home and only one OS for all. That's why I prefer still to use the Amiga over a PC,(albeit an outdated one) because it's fun to use! not just a work machine.
In my opinion people liked thr simplicity of computing, and usuabilty with wide range of applications, which was what the Amiga offered back in the 80's and 90's.
The best OS next to Amiga has to be for me, Apple OSX which is something which is cool and looks smart!
Microsoft tried to cross the gap between home market and PC work market with 'Home editions' of Windows, and now Vista, but they are waaay too big memory guzzling monsters! > which is why I'd to go back to using a 'user friendly' but effective OS's that isnt memory and power intensive!
As for the Hardware, I like the looks of the EeePC by Asus and think that this less powerful 900mhz hardware with more effective operating systems would bring computing back to it's home domain.
Wouldn't the best way forward be to ensure compatabilty of the old Amigas through emulation and standalone new Amiga OS adapted for the current hardware available?
b.t.w
I had a 1200 tower and A4000(the 4000 was cool) but these were big boxes! back then I sold both for about 40 quid, ach.. little did I know what prices would be now, and the popularity of the Amiga! doh!

As for the name, I would evolve that one too, to avoid the likes of Amiga inclined (inclined to do nothing!)
:-?
Maybe something like Amika, or similar :-D
blah.