As some have mentioned already, my advice would be to join a good wine club. The buyer/sommelier will provide you with a few bottles every month that they have personally selected since they get to taste hundreds of different wines from across the globe every month. A lot of these clubs will focus on a different wine region each month and offer you a few differing wines (with tasting notes) that showcase the spectrum of wines available from there. Plus there are hundreds of books available to read if you want to get a bit deeper. If you go to a store, make sure to ask the wine buyer for their recommendation since they will probably have tried all the wines on the shelf and can help find a wine that fits with your personal preferences. If you just go to the supermarket on your own, you end up buying the label, not the wine inside.
I should probably mention that I sell wine for a living. Like most, I never really understood all the fuss until what I like to refer to as my "wine epiphany". I was in my late 20's and working in a nice restaurant in San Diego when I got the chance to taste a '97 Chateau St. Jean "Cinq Cepages" and it literally stopped me in my tracks. Now I had tasted many wines before then, and had liked some and disliked others but when I tasted this wine it instantly clicked in my mind that "ahhhh...now I get why some people are so in to wine!". I wanted to write poetry about all the flavours going on inside my mouth and the weight and delicacy of the wine. The finish lasted for a good 20 seconds and instead of polishing the glass off I nurtured it for a good hour as I didn't want it to end (and I couldn't afford to buy a bottle on my own!). Since then, I have tried to shop at reputable wine stores and explored the diverse offering of wines with help from the store specialists since it is impossible to choose a nice bottle by it's label (and price) alone.
The most important thing to remember when drinking wine is to enjoy it. If you don't like it that's fine. Try something different next time since there is such a myriad of flavour profiles for you to experiment with. Most wine is for drinking, not eulogising (as I did above

) about. Treat it the same as trying a different style of beer. There are so many wine officianados/snobs out there who tend to cast this perception of wine as some sort of mysterious object that only they and their friends really understand. It's complete flimflam. Wine is made from grapes, it's that simple. Treat it as you would any other beverage.
oh, and to answer the OP's original question, the "fuss" is based upon the fact that a well-trained grapevine can provide juice which has move flavour compounds in it than any other fruit or vegetable, which when combined with a world-class winemaker can become the most complex drink on the planet.