Ha! I know, we can go a lot of different directions. I think she'll be a villain. Dany's leadership hasn't been too great, which is a reason she would need Tyrion, as she's also shown bloodlust. She has no problem burning people alive and enjoys it... Sound like someone else?
I don't believe it is her birthright, her family lost the throne in war to the Starks and Robert. Her family took the throne the same way. When she tried to recruit her husband Drogo to invade Westeros, which he really didn't want to do, her reasoning, what she kept telling him, was specifically to rule the world, to rule the seven kingdoms. Her goal was for complete and total power for her and her son. Remember his speech about raping, murdering and enslaving the people of Westeros? She just gave the SAME speech sans raping and enslaving, in the last episode.