I'm going to throw out some suggestions, but I'd love to hear other ideas in the comments!
Sweeter wines...There are certainly lots of sweet wines on the market (I'm looking at you, Moscato and White Zinfandel... I've even been asked for a sweet malbec! Apparently such thing exists!) but these are often overwhelmingly sweet, syrupy, and lacking in any sort of complexity or flavor. They are WAY too sweet to drink with food, and will leave you hurting the next day if you don't drink enough water. Not worth it. So, what ARE some good ones?
1. Riesling (sweet or medium-dry.) With its floral nose, a well-balanced Riesling can be the perfect starter wine. If the acidity is right, the sugar will not be cloying, but neither will it be too bitter or too tart. Canada, Germany, and Austria in particular have some great, well-balanced versions, but you can also find good ones in the US.
2. Brachetto. This guy is a little more rare, and is actually a red. It usually is a little fizzy and on the sweeter size (it is compared in style to a Moscato di Asti a lot, but I think it has more to bring to the table.) Whereas lots of sweet wines are pretty one-note, this guy has a little bit more complexity. Now, for me personally, it is usually way too sweet. I'd have it as a dessert wine, but not on its own or with a meal. That said, if someone is really anti-wine, they might still love this one (and you can always use it to hook them and ease them into other stuff.
3. Gewurztraminer. This one can be cloying. It has very floral aromas and can have pretty high sugar content. That said, one that is medium dry can be just lovely when you've got a sweet tooth. Ask for one that's not so sweet next time you're out shopping.
Now, onto the less sweet wines... Some people who don't have a sweet tooth might be a little easier to introduce to wine, so which should you give them?
1. Pinot Grigio: Trying something mild like a Pinot Grigio might be the way to go. I sometimes criticize them because I think they taste like "white wine." They're a little boring for my taste, but perfect as a gateway wine because they're pretty inoffensive, good with food, and abundant.
2. Sauvignon Blanc (from anywhere other than New Zealand.) Sauv Blanc tends to be juicy and fruity, which can really appeal to a wide vareity of people and food pairings. I only advise shying away from New Zealand versions because they can be super grassy and vegetal, which isn't everyone's cup of tea.
Rose: See, I love a dry rose and think they're perfect gateway wines for people looking to head toward red. They go with anything and are also great on their own. Try one from Italy or Portugal for a fleshy, fruit-forward version. For a milder rose, try one made from Pinot Noir. (However, many of the roses on the market are VERY sweet. Icky. Sugar added- jolly rancher in a bottle... Make sure you're picking a drier version.)
Reds: Introducing someone to red wine can be a tricky process. If they are solidly on team white, then you at least know they're wine fans and can proceed accordingly. I'd recommend trying a fruitier wine like a Merlot, or even a lighter bodied wine like Frappato (though they're certainly harder to find) or even a Gamay. If they're more adventurous, you can start getting them into juicy and spicy Syrah/Shiraz, Cabernet and beyond. Some of you might think I've forgotten Pinot Noir- I haven't- I just think its earthy funk is a little bit more of an acquired taste than those I've listed here. If you have your heart set on Pinot, try one from California or Australia as the warm-climate versions tend to have less earth and more fruit going on.
So, next time you're in mixed company (wine lovers and future wine lovers, that is) these would be my recommendations of wines to bring. They'll hopefully appeal to everyone- what are your recs? What did I miss?