As long as you flash a virgin eeprom with your new hard drive and lock it you wont be banned from xbox live. Although if you don't have one it may be extremely hard to come by one today. If you have played live with the 8GB hdd you must use that one, unless you get a virgin eeprom in conjunction with the new hard drive. If you dont do this your xbox will be banned for a few days and your gamertag will be flagged.
You can recover your account on any xbox or 360 unlimited times on any console. You will need a credit card associated with your 360 account to recover it on your xbox1. After you recover to the xbox 1 you can just delete the credit card info via xbox.com or your dashboard.
I would get the biggest and best IDE hard drive, generally speaking IDE hard drives are hard to come by, but they are a decent value, you might as well buy the biggest one. Ive been using the seagate 750gb barracuda IDE hard drive for over 3 years, its lockable, fast and reliable. I also still use live with this hard drive on my xbox 1. Although its time for me to get an even bigger hard drive now since i filled it up
I would also recommend an 80 pin IDE cable too!
You should be able to use your existing gamertag as long as your gamertag was not on a console that has been previously banned due to hardware modification. This would mean your account is flagged.
Hopefully that answered your questions.