It can be on the same account or a different one, that's up to you. However, if you don't want to keep logging in and out all the time to get to each one, I'd suggest you keep it on the account where you have your primary blog.
All you need to do to make a blog private is either choose that option upon signup or afterwards, go to the dashboard for that blog, then unders Settings choose 'Reading'. Then click in the " I would like my site to be private, visible only to users I choose" option, scroll down and click the Save Changes button.
A new, private blog is only visible to you and to anyone you invite to view or use it. Nobody who views or uses your other blogs will have access to it unless you grant them permission.
This gives information about creating and registering a new blog:
This gives information about privacy settings: