If it's your first job I can understand not wanting to make the situation awkward, but some advice you should take with you into the future: jobs don't owe you anything. If anything they should be thanking you for time served. If you wanna leave, that is your prerogative, and you should do it whenever is in your best interest.

It's courteous and professional to leave a two week notice, and some other office jobs require a longer notice, but not every situation will allow for it.

I would just be honest and up front that you have another job lined up and you were putting in your two weeks, before during or after your one on one, doesn't really matter. If you really wanna be honest then give your manager some feedback of your own and explain some of those reasons you feel like leaving. But it will happen with every job eventually so my advice is just be honest and time things so they're right for you, not the company you work for.

Jobs are a contract between you and your employer. It is 100% ok to find the employer unsatisfactory and move on, it's nothing to feel bad about. Find the place that fits you best. Happy employees are better employees regardless, so by virtue of being unhappy with your situation you're probably less productive anyway. That's just how it goes. You don't have to openly address it with your SM, you're allowed to give your resignation with no explanation. All that said, being with bux this long you might consider a transfer before a different job unless that job is significantly better for you. Sometimes just a change of scenery is helpful, different stores have had vastly different feels for me at least so it may be something to try before you turn in your apron.