It looks like cotton, I'd definitely wash it first, but I'd plan on always air drying it, especially since you don't have enough to experiment with. Unless there's a significant amount of polyester mixed in (which would be quite likely from the 70's, 80's or early 90's) I'd expect significant shrinkage. A 35% or 50% blend would prevent that.
If the top isn't very structured, grain isn't always a huge issue, however if there is significant poly mixed in, it will probably always return to it's original shape. That could be problematic.
It's very pretty fabric. I'd cut the top with the "stripes" running vertically and hope for the best avoiding the wonkiest parts as much as possible. Quickly baste shoulders and sides together and walk around the house for a bit to see how it feels. If it's not pulling great. If it is, you may be able to use bits for accent pieces on something else. Or add a different fabric to the top you are planning to make to begin with.
Edit: looked up the top,if I saw correct one, it's quite simple and unstructured. I'd keep the lines as visually vertical as possible and try to ignore the grain and hope for the best. Sort of like hanging wallpaper on wonky walls - make it look right and try to work around "the rules".
Otherwise, the fabric will just continue to take up space. It would probably make a cute t-shirt for a child otherwise - could be donated- But I'd go for it!