What, exactly, are the supposed health benefits of red wine?
Am I correct in thinking that a dry wine has lower carbs than a sweet wine, and also lower in glycemic index?
Which wine would yield the greatest health benefits and the lowest carbs and glycemic index?
Alcohol is metabolized preferentially to everything else anyway, so I’m not sure it makes a difference, but you’re right–dry wines have fewer carbohydrates. Check here for details.
Also, as the linked page mentions, alcohol is seven calories a gram, so watch yourself.
The theory on the health benefits is based on the antioxidants in wine. There are conflicting studies on red vs. white on this score, so it may be red or either.
Some sources say a full-bodied red goes with peanut butter and jelly. 
Jack Spratt could eat no fat,
His wife could eat no lean,
But with a glass of good red wine,
They licked their platters clean.
From here:
“Research does support the idea that part of the lower rate of heart disease in France may be due to wine. Natural antioxidants in wine, which are also found in tea, grapes and other fruits, help keep LDL (“bad”) cholesterol in a less-damaging form. Other research suggests that modest consumption of any type of alcohol is linked with healthier levels of a marker for inflammation than seen with either complete avoidance of alcohol or consumption of more than two drinks a day.”
More here.