What Keywords to use?

I think this would be kind of hard to determine, since (at least I'm not aware of) specific analytics of how a user finds an app within the App Store isn't known.

This is also specific to your game. I think you want to find generic yet descriptive terms for your game. You would probably avoid a keyword like "game" since I feel it's rare that someone would search for the word "game" in the app store instad of just selecting the 'Game' category. Not to mention, every game will probably come up in App Store search results with that query. But maybe if your game for example is a fighting game, you would use the keyword 'fighting' since that's a specific type of game that is commonly searched for.

There is no point in using your app name as a keyword, since your App's specific name is already searchable.

Basically, I would visit some iOS game web pages, and even some traditional PC/console game websites and look at the keywords in their HTML source and descriptions they use. This may be identical or close to what they use on the App Store and give you some new ideas as well.