I always grow my melons vertically, on metal fencing, although mine is anchored with T-posts in the middle of the row in the garden. You should be fine with one caveat, any melons growing behind the fencing, if it is close to the wall, may get stuck.
As long as you're using regular fencing material it shouldn't rust. Rust won't really hurt the plants, but it's not the best having to reach into for harvesting.
I also use slings made from strips cut from old t-shirts to hold melons as they grow.