If you want sweet red, Sangria is a good choice. Moscato or other sweet reds are too sweet, IMHO. (And I drink a lot of wine. A lot. Probably too much.)
There are nice sangrias you can buy pre-made, or lots of recipes for making your own. If you're just going to have it occasionally, you might want to go that route since you can put in exactly the fruits and etc that you want to make it have all your favourite flavours. It will keep for a while once you've made it as long as you store it tightly and in the refrigerator.
That being said, if you're drinking it for the health benefits, the sugars in a sweeter wine will probably negate the benefits (also, you're way more likely to get a hangover the next day if you drink sweet booze). A dark red wine is best for the antioxidant resveratrol. Maybe try a few Merlot, Malbec, or Pinot Noir varieties and see if there are any you enjoy. And don't think the whole food-pairing thing is for snobs and it's all hooey--there really is something to it. Have a platter of cheeses, crackers, dark chocolate, and maybe some veggies + dip with it. I've had wines I thought were unpleasant, but with a nibble of a sharp cheese between sips it tasted totally different and was very nice. Experiment, find what works for you, and enjoy!