There is a bewildering variety of wine glasses available. The companies marketing the glasses have a vested self interest in convincing people that you need a different kind of glass to properly enjoy each kind of wine. According to some of them you need a different glass if your Sauvignon Blanc is from New Zealand versus France. This is nonsense. The proof is that most professional tasters use one kind of glass. This is usually a tulip shaped glass with a stem and a wide enough top that you can get a good sniff of the wine.
Using one kind of glass is great if you are trying to objectively compare wines. If you are on a tight budget or lack space an all purpose tulip shaped wine glass is a great start. I do prefer glasses with a stem, particularly when drinking chilled wines. If I were adding to this I would go for a Champagne glass, either a tall thin tulip shape or a flute (narrow angled straight sides). These allow the bubbles in sparkling wine to take their time rising through the glass. In addition to being nice to look at it slows down the process of the wine going flat. They also can serve as desert wine glasses.
For most people that will be more than adequate. Professional wine service will often include having white wine glasses that are smaller than red wine glasses, which are sometimes more bowl shaped, and desert glasses which are smaller versions of Champagne glasses. I have a hard time seeing a reason for anything more unless you just like glasses.