Looking at it a second time, there is another reason you might want to go Horizontal. First, if you are thinking of hanging it on a wall, you would want to get your anchors into the studs for extra strength. If the frame is as heavy as it looks that would be a lot of weight that needs to be distributed on few points. If you go Vertical, you would probably have to anchor, or suspend, all the weight by 2 or maybe 3 points based on studs being 16" on center. By going Horizontal you would have the possibility of more anchor points Maybe 4 to better distribute the weight. That would mean less weight per point or hook.

It also would depend on where you want to put it. Between windows or over the back of a sofa. On a large wall or short wall. What furniture etc. you will place around it. If you do go Vertical I would not only hook it to the wall to keep it from falling over but I would also put something under it to support it. Maybe a small coffee table height stand that you could display other items on.

Maybe take a couple 2x4s. and measure out the length of the frame. Put one flat against the wall and anchor well into the wall. Then take the second 2x4 and attach that thin side to the wall, into the other 2x4. Sort of a sideways L shape. Like your window ledge. Then use a couple standard picture hooks to keep it from tilting off. You could stain, paint or finish off the piece to match your wall. Maybe put a little moulding around the bottom 2x4 to finish it off. If the frame is that heavy that might be a good way to support it.