All of account info is stored on the Xbox Live service, so the information (such as credit card info) will remain on you gamertag, but it will be removed from that console. You can then move you gamertag to your new console.
I suggest moving your gamertag from the Arcade console onto a USB stick, as well as any saved games you want to keep. Then you can plug that USB stick into you new console, and transfer everything straight over. Also, all
the account information will be removed from your old console, so no one can get access to it when you trade it in.