1. A "quick start" that skips all the splash screens, intros, and takes me directly to the "choose game" screen (play game/options/exit game/etc).
2. A "quick game" button that puts in entirely random options for everything but difficulty level, then throws me into a game.
3. A "quick PBE" version of the game that opens up a dumbed down, graphics unintensive version of civ that allows me to take my play by email turn without booting up the entire game.
4. An "advanced player" interface, which does what #1 does as well as puts the game creation information all on a single screen. Custom games, regular games, multiplayer, some options, etc could all fit on a single screen if designed correctly.
The thing I've always despised about Civ4 is how long it actually took to get into a game using the default game install. Using the icon to enter a game, I'd have to wait for the game to load, then click through all the intro screens (no flavor on the intro screens either), click play game, go through all the options, and finally get in. Most of that could be done away with.