If an effect instructs you to put Game Trail onto the battlefield tapped, it will still enter the battlefield tapped even if you reveal a land card from your hand.

You may reveal any land card with either or both of the appropriate subtypes. It doesn't have to be a basic land. For example, you could reveal Canopy Vista from the Battle for Zendikar set to satisfy the ability of Game Trail.

Lands don't have a subtype just because they can produce mana of the corresponding color. Game Trail itself is neither a Mountain nor a Forest, even though it produces red and green mana, so you can't reveal one to satisfy the ability of another.

If a Mountain or Forest is entering the battlefield from your hand at the same time as Game Trail, you may reveal the other land to have Game Trail enter untapped.