The games should, in my opinion, feel similar to HTR in terms of gameplay, as that was one of the greatest adventures of all time, and have the same awesome voice actors. It should be grittier like the comics, though, which is something Telltalte has announced that they're aiming for. They will also need a story arc that ties all of the games together, to make them more interesting to play and to give players a greater reason to buy the next game.
Also, it has been announced that Sam and Max will be harder than Bone, as it is for the adventure gamer crowd instead of the comic-fan-who-has-never-played-a-game-before crowd. And yeah, it needs some good minigames and great dialogue, but that goes without saying.
I agree with all these points! I don't really care about the minigames though, just give me some good puzzles and don't tell me what to do when I hover my mouse over an object! Give me the option to do trial and error! I want to try to pick up a piano, even if it's too heavy! I want to try to talk to a wall, even if that doesn't make sense! When the game automatically picks your action when you hover over an object, you're not really figuring out anything more than just going through the motions.