I know that it's an interview at a deli,and not at a bank or something similar,but you want the job,right?You don't have to go in a power suit,but you're not a kid anymore,so try a nice pair of black dress slacks,blouse and a nice pair of modest heels,like a 2-3inch black pump.Voila!You show that you know how to dress grown-up and professional when you have to,which is also being respectful to the person interviewing you,they'll be impressed.It may also put you way in front of the "kids"who'll show up in flip-flops and chewing gum,you know?Also,leave the cell phone in the car!Seeing that you're not afraid to dress professionally just may move you up faster to any sort supervisors or managerial position,as well.Good luck!
If it were me, I'd wear a white apron smeared with copious amounts of ketchup, and one of those hats that looks like a quarter round of cheeze. The kind those football people wear in Wisconsin..This would send a clear message that your always thinking, and also, that you are not averse to humiliating yourself for your job.
If you can remember what the staff wears and wear something as close to their uniform as possible. Avoid showing up in something you might look great in at the club, it might send a message that you are not taking the job serious.
White shirt, fitted black/navy/brown trousers or a skirt which is knee length or mid thigh.
Black or nude tights and black court shoes or flats.
Optional- A blazer or fitted coat which matches the colour of your trousers or skirt, very simple jewellry, a bag and a watch which gives the impression you are punctual- make sure it's on the right time.
I don't know what job you are going but adapt it to the the job, if it's a less formal setting you can get away with a white t-shirt with the fitted trousers/skirt.