Good question, and I agree with most of what Cherib603 wrote...my minimum gap is 1/2 inch square - so if it's wider than half an inch, yes, I'd reduce the height of the gap to 1/4 inch. In other words, I think half inch by half inch metal hardware cloth is good. But if I have a seam, say a gap between two 2x4s - I would not want more than a quarter inch between them.
I used a combination of screws with washers to attach the hardware cloth, but then in between them I put the U shaped nails for extra attachment. And I spent hours trying to think like a predator as I was designing and building. When all was said and done it did not take me that long to build the pen and it has lasted over 6 years so far. We are in the process of building the second pen.
We have saved up and will be using mostly pvc-coated half inch metal hardware cloth, 16 gauge. Including across the bottom.
Pen I has coated chain link across the bottom to prevent larger animals from digging under and in (in New England there are so many stones that digging a deep trench around the pen was not going to happen). I fastened the edges of the chain link between two one by sixes that frame the bottom edge of the pen. Vertical posts (3 sistered 2x4s) are attached to that frame, and across the tops of the verticals are 2x8s. There is a distance of 4 to 5 feet between verticals. I accounted for snow load.
That's not the entire set of details, but what I felt you might find most helpful.
What I plan to do differently this time - Taller pen. Pen I is a meter tall. Not a problem for me - I am 5'3" and very agile for a junior senior citizen. So I go into the pen, and duckwalk around, dumping swim pans, gathering the occasional egg, scooping up a duck who needs to see the vet, etc. But try to get help for that! hah!
So, next one will be about 6 feet tall. It's going to be 6 feet at one side, dropping a foot on the other so that if I decide to cover the pen, snow and rain will drop off (always thinking snow load here - we can get 3 feet of snow in a day).
Something I love about Pen I, that I got right, is making sure there is a 2% slope across the whole pen. Rain and swim pan water will not sit in a puddle. We are also blessed with a fine sandy loam soil that drains moderately well.
The night pen is in the "barn" in the walkout basement. I have two flocks. One flock has access to a shelter when they are in their day pen. The other only has a small area with roofing over it (the two flock thing came up after I built the pen, so that was not incorporated into the design and we ar making do.)
New Pen will have shelters in each section. I am still designing this, and trying to decide between small plywood A-Frames or mini greenhouses.
Pen I is under a sturdy sugar maple. It provides shade, absorbs water and manure, and shields from hail and heavy rains.
Pen II is partly under a hickory, so we'll have some shade and shelter, but we'll have hickory nuts in late summer - the pen will have fence across the top so that won't be a problem. Pen II is also on a slope, a bit more than 2%, and also has a nice loam underneath.
Improvement - I am figuring out how to change the swim pan dumping situation not so much for the water runoff, but for the feathers and muck that get stuck in the fence. So far my plan is to put drains in the swim pans so that rather than lifting and dumping, I can turn a valve and empty them that way. The pipe will be large enough and short enough to avoid clogs.
Some polywire electric fence is something to seriously consider. There are solar chargers, and small battery or home electric powered chargers, and electric fence is not difficult to install. I did it. I was crazy nervous at first - but I had worked with folks who know how it's done so I chatted with a couple of people first, then got the materials I needed and set up a fine fence. At least two raccoons can attest that it worked.
I use keyed locks on the gates. Raccoons aren't the only ones up to mischief at night.
The base for Pen I is a nice compost. Made from duck manure and chopped straw. I don't have to add straw very often, and it becomes beautiful stuff for the garden. Under the swim pans is sand, smooth pea gravel, and sometimes oak leaves to reduce odor in summer.
I am switching to hardware cloth underneath because occasionally burrowing rodents come in from underneath, at night through the chain link. I don't want ducks turning their ankles in the holes, so I have to fill those in. One more maintenance chore I would rather not spend time on.