Publix's slogan is "Where shopping is a pleasure," and they live up to the claim. OP, you've indicated that you'll be going to
Walmart. Just consider that for sandwiches, Publix offers Boar's Head cold cuts, which are about as good as it gets and often a healthier alternative. You pay the tiniest bit more, but nothing compared to Disney counter service.
Publix's meats are higher quality than Walmart, plenty of selection for grilling. They also sell prepped meats, like chicken flavored with lemon pepper, marinated beef, etc , which on vacation can save you by not having to buy seasonings. Just put it on the grill.The fish counter is offering a service where you choose your fish and your flavoring; they prep everything, and put it in a container that you just put in the oven. Again, on vacation that can save you money and time.
The Publix deli is fabulous! You can get rotisserie and fried chickens, mojo pork, wings, etc. all ready to eat. There's plenty of salads to choose as sides (macaroni, potato, etc). There's also hot sides like Mac and cheese and potato wedges. I always find the prices reasonable for a quality meal. The subs are to die for, too. Save money by ordering a whole sub and splitting.
To save money at Publix, buy the generic Publix brand. It is considerably cheaper and at the same quality level as name brands-- no matter what item you're talking about. I've tried Great Value from Walmart and the Kroger/Winn Dixie generics, and I'm always disappointed. Once I buy the name brand at Walmart, I'm at the same price as the generic at Publix, so I've learned through a lot of trial and error that Publix is a better value in the long run, and I avoid Walmart's insane lines around the, invariably, two open registers.
If you haven't tried it before, seriously treat yourself to a carton of Publix ice cream! That and the Publix brand fat free blueberry yogurt, I don't think I want to live without.