I'm with the "Plug it in, plug in game, play game" crowd.
Maybe instead of using a disc, the game could use some sort of (formatted to "only interact with the console") data stick (Like a USB drive) that plugs into the front end, complete with (translucent, so you can see what's in the slot) hatch that you could snap down to protect it from The Cat or Accidentally Kicking It.
This will make the game more robust, and only marginally increase
Internet Connection would be completely optional, of course. You can definitely play off-line, and the only difference between Free Online and Premium Online will not be "Multi-player actually exists, now", and will instead be "Pay to get rid of advertisements".
If I want to get REALLY FANCY, I'd probably give it some way to interface wirelessly with your PC, to cut down on awkward A/V cables stretching across the house when you want to plug 'n' play with Steam Big Picture or watch a DVD or something (Put DVD in computer, enable connection, sit down in front of the TV to enjoy the movie).
But, hey, I'm a laymen. What do I know? Besides What I want.
Oh, and as far as aesthetics go, the console itself will be a featureless box. I might be tempted to include some divots on the side to hold controllers, or else attached the controllers semi-permanently to the console, itself, with some sort of self-spooling wire for neat storage, but still allow third-party manufactuers to make paddles.