They would have chose Rhaegar. It's in the lore that the Tourney at Harrenhal was pretty much accepted as a way to gather all the great houses together in secret away from the Mad King. But the Mad King, who hadn't left the Red Keep for years, got wind of the plot (from Varys) and attended, ruining Rhaegar's plot.
http://gameofthrones.wikia.com/wiki/...y_at_Harrenhal