I would go much smaller than 1x3" welded wire - raccoon hands, rats, etc can easily fit through that. I would go 1x1 on the sides of the run; 1/2 x 1/2 in the coop (windows, etc) where you lock them in at night. I used chicken wire to top my run - heavily overlapped - and zip-tied it together, before putting about 4" of dirt in for the bottom; heavily overlapped and zip-tied as well on the top. Top and bottom wire is both heavily secured to the wood "baseboards". (My objective was to literally create a solid framework of wire enclosing the run.) If you used 1x3 on the top of the run, and your hens were locked in a coop at night, you would probably be ok. You may see rats and weasels, however.
Since I lock my hens in the coop at night, I was not too worried about nighttime predators coming through the top of the run, which they probably could, but would not be able to access the hens in the coop.
I have had weasels and rats try to access run at night (likely for the food in the feeders) - they dug significant holes under the run but thankfully could not breach the wire underneath. (I have since gotten rid of the predators, but wow, they can excavate a TON of dirt in just one evening.)
The sides of my run have a base board, "mid" board and top (2x4s) where I have securely u-nailed the 1x1 wire. And attached the bottom and topping wire as well.
I have no idea how to attach a pic of my run and coop, but would be happy to send one to you. If interested, let me know I can email it to you seperately.
Good luck, and have fun!