I saw on TV a wine rack in a built-in wine cooler (room).
It consisted of two steel bars about 3/8" - 1/2" in diameter that were placed horizontally about 2 - 3 inches apart. The ends of the rods were inserted in drilled holes in the walls. The bottles rested on the two rods and the label was clearly visible.
For a single row of bottles, I think 1/2" wood dowels between two 6" wide boards would work fine.
The build would be a picture of simplicity. Stack the two boards. Mark the locations and drill. Then cut the dowels to length, glue and insert them in the drilled holes.
As I recall they had some paper tags hanging from a few of the dowels. I have no idea what information was on those tags, but the attachment was really easy.
This is similar to what I saw on TV. In this case it is all welded construction.
I've made two two wine racks in my life. One was for my kitchen and consisted of three vertical boards spaced widely enough to accommodate a single stack of bottles. I nailed and glued 3/4" x 3/4" cleats on both sides of the vertical boards to support and space the bottles. It turned out to be a royal pain to apply a finish to this, though after it was done, the function was fine.
The second was a vertical panel that attached to the wall with a series of short horizontal shelves. To keep the bottles from rolling off the shelves, I added a 3/4" x 1-½ strip to the front of the shelf, with the 3/4" lip keeping the bottles from falling off the shelves.
It was not particularly space-efficient and it took an inordinately long time to assemble.
