Putting in my 2 weeks

I got hired for a new/better job and am waiting on my background check (it has one iffy charge but it has never been an issue for any employer) so I'm not too concerned about it. They're having me start training already though so when the background comes back I can start right away....but I still don't know when to put my two week notice in to my current job...should I do it now?? Since I'm gonna be doing some training? Like I said, it's never been a problem but I'm worried the one time it may be then I'll be assed out of a job.....any suggestions or advice?