The Rock & Austin
 

When did each of these two win their first WWE Championship?

Stone Cold won his first title by defeating HBK at Wrestlemania 14

Rock won his first by defeating Mick Foley in the finals of the world title tournament at Survivor Series 98. (the title had been declared vacant after kane and the undertaker both pinned SC at Unforgiven [i think] in a triple threat match.)

Foley lost via screw job I believe.

Yeah, it was SS 98 and Vince "screwed" Foley out of winning it.

yes, that is correct...rock put foley in the sharpshooter correct? and then vince came out and rang the bell and rock turned heel again