onyxelle, let me start with my favourite definition of what a "good" wine is: it's the one you like. While there are a lot of wine snobs out there, it's really not necessary, just like the supposed rules about white wine with fish, red with meat also don't apply today.
As for the different glasses, they are designed in order to concentrate the different qualities of each wine, and direct the wine to the optimum parts of your taste buds, to enhance the experience. Check out this site for more info:
http://www.riedelcrystal.com/index.htm This is the prefered crystal for connaissouers, and the ones we have (Vinum line, the hand-made Sommelier's series is just priced out of our range).
I don't know how sweet you want your wine, but there are a couple of Greek dessert wines that are good, and not expensive. There is the Samos Muscat (white, sweet) which I sadly haven't seen lately in these parts, and Mavrodaphne of Patras (red, sweet). As for blush, or rose (pron. ro-zay) wines, I prefer the dry variety, so I can't suggest some sweet ones. I also have no idea what Publix is, but I assume it's an American grocery store?