When I thought about the party screen in this game, the first thing I thought of was the party screen in Colosseum with the headshots of each Pokemon, so yeah, we'll definitely have something like that.
I'd like them to change the way the party screen is organized. For a long time, we've had three on the left and three on the right. I'd like them to change it back to how it used to look in the Game Boy games, with all six stacked in a column. It only makes sense now that we have triple battles. This way, it's easier for all players to tell which of their Pokemon will be sent out in battle, because they'll be in a neat tiered order. The Pokemon's name, gender, and level would be on the top half of their box, and their HP and status would take up the bottom half.
Another thing I'd like to see is instant drag-and-drop. Imagine being able to drag your Pokemon to the spot in the party where you want them to be, and if it's placed over another Pokemon, those two Pokemon swap positions. You wouldn't even need the Switch command on the party screen; this would be so much simpler!
I'd also like for us to be able to physically see our held items on the party screen, rather than always seeing that green can, because all too often I forget which of my Pokemon is holding which item when I'm constantly exchanging EXP Share among every member of my party. Also, the Move Item feature was awesome in BW2, so I'd like to see that go one step further by allowing us to not only drag-and-drop our Pokemon, but our held items as well. There could be a held item slot to the right of each Pokemon; tapping on it would give you the option of exchanging the item for another item in your bag (or adding one if the slot is empty).
Since the top screen went largely unused in BW(2)'s party menu, I'd also like to instantly view a Pokemon's status on the top screen when I tap on that Pokemon. Just press L and R to flip to different sections of the status screen. Then you wouldn't even need a status/summary option, because your Pokemon's status would be right there on the top screen. They could bring back the option to rearrange your moves, allowing you to quickly drag-and-drop your moves. So basically, I'd like the new party screen to be as streamlined as possible.