I don't want to spoil too much for you, but if you dig Tywin, you'll enjoy the Arya chapters in Harrenhal in A Clash of Kings, she serves as his cupbearer, and Tyrion's chapters in A Storm of Swords, especially during the trial. Tywin is likely in my top 5 favourite non-POV characters. As for Roose, you'll have to wait until A Dance with Dragons, we get to see his total badassery from Theon's perspective while they're in Winterfell. Some characters and moments to look forward to would be Wyman Manderly as he's just pure genius hidden behind thick layers of fat, Stannis (he's just so much more than showStannis, easily my favourite non-POV character), the Dorne plotline is just so brilliant in the books that I won't even bother comparing it to the show, the Greyjoy plotline in A Feast for Crows and Jaime's redemption arc in AFfC and ADwD. All in all, you are in for a fantastic read. I'm sad I can't just wipe my memory and read it for the first time again. Oh, and you'll likely re-read the entire series once a year and always notice things you didn't catch the first time which is a thing I really love about ASOIAF.