While chicken/poultry hex wire could possibly work ... it has many disadvantages compared to welded wire ... listed below.
Poultry/chicken wire is usually 20 gauge or smaller/thinner (size of wire gauges are the smaller number, the thicker the wire)
20 gauge wire is 0.0320" in diameter.
14 gauge wire is 0.0641" in diameter.
14 gauge wire is slightly more than twice as thick, and probably 3-4 times as strong as the thinner 20 gauge.
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One ... disadvantage is it is harder to see ... so, a dog can just run right through it, just like a screen door!
Two ... as it is thinner/weaker it is easier to rip/tear/chew through ... doesn't take long!
Three ... a little time ... and, rust ... and it will need to be replaced.
Four ... Welded wire is actually welded at each junction, and poultry wire is twisted ... so the junctions are weaker too.
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In my post #4 above I suggested welded wire, as not only is it stronger, but a good visual barrier, while some dogs, and most coyotes and foxes can leap over a 5' fence ... they will usually try to take the easy route ... and more sneaky, stay out of sight route, and check out the fence for weak spots, or a place to go under ... they use their nose alot ... Mr Sparky likes to say howdy to wet noses!
Your proposed run size is really only 210 linear feet ... while bigger than a lot of the small runs we see here ... Large to "me" is over 150' square (half acre) ... I'm glad you specified actual numbers ... but, where do you live?
With adding the hardware cloth to the bottom, you also stop, (or divert) snakes and possibly mink too depending on which size of mesh you use for the physical visual fence.
If you choose to skip the electric fence ... then I'd recommend the "skirt" fencing mentioned above ... but, lots of critter will just climb over a 5' fence ... with electric, once a critter meets Mr. Sparky ... they stay away from the fence ... no trying to dig, or jump/climb ... OUCH!
Buy once cry once ...
If it is worth doing, it is worth doing right the first time.
A good fence takes just as much work to install as a poor fence ...
A good fence is a one time expense, not like that bag of chicken feed.