I think when you click "go to next game" they are brought up in the order in which your opponent made a move, from oldest to most recent.
If you click the "My Games" link you will be taken to the folder that shows your games, and from there you can select which game to go to. I keep all my active games in the inbox folder, but you can use "manage games" to place them in other folders as well.
Under "My Games" you can select how they are listed using the drop-down box at the top. you have 9 options including "least time remaining" and "most moves" which seems to be what you are looking for. To the left of that selection box is 3 options of how the games are listed, including one that show a mini-board of the current position.