I just accepted a new job & immediately thereafter was offered another one that I know is more important to the start of my career. I cannot turn this down, despite that I just underwent a week of training & am desperately needed at my current company. I do not know my boss well enough, nor have I been there long enough, to worry about using him as a reference, but I do not want to leave them scrambling to find a new employee. The better job will start in two weeks. WHAT SHOULD I DO? Two week notice? Email resignation? Etc.

Why not just tell them in person your dilemma and come clean. Email is the chicken way out. You need to tell them immediately of your decision. Deception on your part and staying until your new job starts is essentially wrong. If you do this the right way the company will have plenty of time to get a replacement for you since they just interviewed probably half your town. Be a grownup about this, please. No company likes to hear that you've found a better offer, but stuff does happen in the real world. At least you will have enough maturity to tell them in person.

Never resign in a email always do it properly, and alwas give notice when you can.

And remember you may not list them, but in some jobs, such as government jobs or jobs where you have to provide income tax records perhaps. Or where they do credit checks and the job may show up.
Add to this that the boss at the place you are not quiting may be a boss for a future job 20 years from now and remember you