For Stage 1-10, I recommend you to use LIGHT monsters, high level monsters, and trap cards to get Mako Tsunami, Ishizu Ishtar, Odion to appear at the Gate earlier. You can easily win victories using such cards since Standard Duelists uses very weak decks at Stage 1-10.
Which card should I trade to complete one of Stage 7 missions?
Just trade cheap card that you can trade spending only Gold and save trader items for getting good cards near future. I strongly recommend you to trade Mythical Beast Cerberus, but you will not have enough trader items at this points.