IMHO, personal grooming is one of the most important things to look classy. It's all about subtle make up and avoiding anything fake: long fake nails, fake eyelashes and obviously tattooed makeup. I mean, you can have fake nails and fake eyelashes, but they still have to look natural. Your hair color is a big one, too. It has to look like it could be your own. I have very dark brown hair, I would never dye my hair red or blonde. Accepting who you are and making the most of what you have makes you look classy and confident: I'm very pale naturally, and I accept that; when I was younger I would try to get a suntan and it was always extremely painful. Now I'm pale and rockin' it, even though I know paleness is not the beauty standard where I live. I just own it and wear shorts!
I love the transformative quality of nail polish, too. On the one hand, neutral colors are always classy (and subtle), but on the other hand, whenever I see someone with beautiful bright red nails, or a vampy burgundy, or a perfectly applied eggplant polish, I think they have gone/are going somewhere fabulous and had to get their nails done, so by extension their lives are interesting. I know it's silly, but that always comes to mind.

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Style wise, everybody's different.
I am a high contrast winter in coloring. My Kibbe type is dramatic classic. There's a lot of structured/semi-structured black in my closet, leather jackets, pants and blouses, and I live in a tempered climate. My basics may not be your basics, but I would say something too sexy/tight/revealing will never be classy nor subtle.
Lacquered nails and jewelry are my obsessions, and I have to have both. Well-made jewelry brings SO MUCH class to your outfit.
And one last important thing to say is that you don't have to be skinny to look classy, but it is very important that your clothes are the right size, not too big and not too small. And if you are overweight, grooming is even more important.