How important is it to you to see the 'famous' characters?
I'd love to see this set in a historical period like Robert's Rebellion or the Blackfyre Rebellion or the War of the Ninepenny Kings, simply because it would allow the writers to have more room to work and explore an underdeveloped time period. The general course of the events in the books is pretty set in stone and GRRM's world is rich and deep enough that there are tons of places that have nothing to do with the main plot of the books that could give rise to a cool new story and interesting new characters, just as TWD did just fine while having very little to do with the TWD comic's storyline.
Yet I suspect a lot of people would be confused if they don't get to see Tyrion or Jaime or Arya or Jon Snow or Dany or any of the other famous and popular characters. It wouldn't be a problem for me, as someone deeply involved with the books, but for the casual fan it might lead them to wonder why they even bothered to call it 'Game of Thrones.'
The best historical era to both keep a link with the show while still allowing room for plot movement that doesn't screw with the main story would probably be Robert's Rebellion. It'd be interesting to see a younger Ned Stark, Robert Baratheon, Stannis Baratheon, Jaime Lannister, Cersei Lannister, Tywin Lannister, etc.
Not to mention Rhaegar.