Publix is the way to go for sure. They have decent prices, and it's a much more favorable experience than the mayhem known as Wal-mart.
I wouldn't eat any meat or perishables from Wal-Mart. I just don't think their stores are very clean.
Compared to the prices in Iceland, you'll be quite pleased.
My receipt from a few weeks ago:
gallon of milk $3.35
50 count Twinnings tea bags $4.75
loaf of Italian bread $1.47
1.5 pounds bartlett pears $2.83
Anne