I agree, I think Virginia is one of the most perfect names. I think some people subconsciously find it overly conservative, or at least I used to, partly because of the word "virgin" and partly just because it seems old fashioned. Now I think it shines with patriotism and feminine strength, and I'm glad I've come to appreciate it this way.
My go to is Virginia Laure, honoring my sister Laura. One of my favorite combos when I was more into two middle name combos was Alice Virginia Laure, which I now find a bit much, but still appreciate from afar. Some more theme-y combos I'm into are Virginia Glory and Virginia Cardinal.
I love the nickname Ginger too, it's snappy and cool. Think about Ginger Frances! But I would be hesitant to use it since I hear it as a derogatory term way too often. I lean toward Genie these days, but I'm also happy with no nickname at all.