I Shared a Xbox With A Roommate But Console got perm banned if i got me a console and kept...

As long as nothing else is done on the new console to cause it to be banned, you're find using your account.

Both my console and account got perm banned.

So my question is if i buy a new console and set up a new account will i get automatically banned by Microsoft? I'm worried that if i spend £200+ on a brand new xbox that Microsoft will ban me straight away because they see my name and address.

Sounds unusual to me considering I never encountered this problem before while playing these games. I would suggest messaging either contacting Treyarch, the Xbox Live Enforcement Team, or an Official Xbox Staff member to find out why you were banned and
or see if you can find a way to get unbanned. If you plan on doing the second part of this solution, be prepared to have reasons why you should be unbanned. Hope this helps you.

When you're banned permanently, an e-mail is automatically generated and sent to the address to which your Xbox Live gamertag is associated with. Prior to any ban, the Xbox Live Enforcement team ALWAYS conducts their own investigations and ensures that there
is enough internal evidence to proceed with ant sort of action. The most that will be released to the general Xbox Live population would be your e-mail.

Sorry, but if the enforcement team denied the appeal, there is nothing else that can be done. They are the only ones who handle bans.