I had kind of the same scenario, had worked at a pizza place for 2 years and got a job offer with better pay/hours in a lab at the university hospital.
Definitely give them 2 weeks notice, if you don't, don't ever try to use them on a resume/work history ever. I pretty much told them that I had a better opportunity and that it was great working there, but I had to go with my better option. Then wrote my two weeks. I still go in a visit sometimes and go into the kitchen to catch up with my old boss. Just be sincere and honest about it.
"Because she's the hero they deserve, but not the one they need right now. So, they'll hunt her, because she can take it. Because she's not our hero. She's a silent alcoholic. A watchful booze hound. A drunk knight." -TechnoPotamus
"she just partied for a week straight in a dress and sombrero." -Rossik
"day time drunk is a gift from the gods" - Timmi