Will my progress on my 360 transfer over to the One?
Yes, via the Cloud
Will my achievements transfer over?
If so will the achievements look any different?
Taken from the official FAQ:
Will I need to re-earn my Xbox 360 game achievements on Xbox One?
No. If you earned an achievement on Xbox 360, you'll still have it when you play on Xbox One.
How do I pick up at the same place in a game on Xbox One where I left off on Xbox 360?
To continue playing a game on Xbox One that you started on Xbox 360, save it to the cloud. If you're already using cloud saves, you're good to go. If your saved game is stored only on your Xbox 360, do the following.
Note You must have an Xbox Live Gold subscription.
On Xbox 360, go to Settings and then select System.
Highlight Cloud Saved Games, press Y on the controller, and then select Enable.
Start your game. When you're prompted to select a device for saving your game, choose Cloud Saved Games.
End your game. Leave your Xbox 360 on long enough for it to upload your saved game. When you play the game again, you'll pick up where you left off.
To confirm that your saved game has synced with the cloud, follow these steps:
On your Xbox 360 console, go to Settings and select System.
Select Storage, and then select Cloud Saved Games.
Select your game.
If it says "In sync," it's available to play on Xbox One.
If your game hasn't synced, start the game, save your progress, and exit again.
Some games (mostly arcade games) will save your game progress to your profile instead of creating a save file. Even though there's no file, your game progress will also transfer over when you change consoles.
Make sure you save your game frequently while playing on the Xbox One. If you open another full-screen app or game without saving, you'll lose your unsaved progress.