Like everything else, Your Mileage May Vary
I have NO IDEA how much "pressure" pygmy goats put on a fence but surely they don't need a lot of height. Chickens put no pressure on the fence but will easily fly a 4' fence, some a 5' and some a 6' ... Though USUALLY they like to land on the top before they go over so you can sometimes solve that problem with a wire above the top of a 4' fence.
As far as keeping the chickens in, cattle panels have 8" wide x 6" high openings except the very bottom where there are two 4" high. My concern is that chickens can likely get through a 6" opening. My solution to that is cheesy
I have a lot of old yellow or orange hot wire rope that was up on wimpy wood posts not deep enough in the ground. I'm filling in the first and maybe second 6" opening with a horizontal run of that stuff. I really don't know how high I would have to go up with that if the girls are intent on getting out. Not sure if they have the ability to fly up a couple of feet, bring their wings in and land on the horizontal wire of a 8"x6" opening. They aren't songbirds after all.
In my experience, limited though it is, chickens will pretty much follow their beaks along the ground if they have plenty to keep them occupied (ie plants and bugs) and nothing exciting on the other side. They may stay inside a fence line without too much extra effort on your part. Another consideration is "what is on the other side"? If there aren't neighbors that would get in a huff if some chickens wandered on their property now and then, less of a problem. And since I think you are home most of the time you could likely keep an eye on them. We let our girls wander the area around the house if we are home. Only Echo has ever crossed the road and that was after the fox dropped her and she ran, blindly I imagine. Some of the girls will go out into the edge of the road, no idea why and not a popular thing with me! That isn't real common though.
If the goats aren't a problem, you can use the strength of the cattle panels to hold up at the corners (put one T-post for each panel 4" from the corner where two panels meet) so you don't need wood posts and bracing like you will for a stretched fence. You will still need braced or concreted posts (bracing here is still good) on the hinge side of gates ASSUMING you are using structural metal or wood gates. Join the panels with hog rings. At
@farmerjan's suggestion, I overlapped my panels one "opening". That makes each joint quite strong but I am keeping out predators and thought I was keeping in a large dog. You may be able to just butt them together and join with cheap hog rings or the $3.50 wire panel connector hinge from Premier 1. Don't try to put a T-post at the joint, that will make it really hard to clip the panel to the post.
You can make a gate out of a piece of cattle panel the desired width and "hang" that with the wire panel connector hinge. I don't think I'd want to make a wide gate that way but would be functional for a 3' or 4' "people" gate. That sort of gate wouldn't need to be hung on a braced wood post. Put a T-Post midway between the vertical pieces at the end of the fence as you would for the end of that panel anyway. If you want a 6' or 8' gate, you could hinge a 3' or 4' piece of panel on T-Posts on both sides. You would need to clip the cattle panel gate high and low.
Note, however, that cattle panels don't do "rolling ground". You'll either have to dig a trough or mount the panel higher on the posts to accommodate somewhat non flat ground.
Sheep and Goat or Field fence frequently comes in 330' rolls. That would be roughly equivalent to 20 Cattle Panels. TSC sells them for $22 each or > $450. Woven Field fence is $150, Sheep and Goat $280. Figure 1 T-post every 10' for stretched fence, I used 1 every 8' for the cattle panel part of my fence. As you noted, a single cattle panel is a LOT easier to move around than a 330' roll of woven fence of any nature. Those rolls weigh ~200 pounds and up vs 36 pounds for a 16' cattle panel. And you can move a cattle panel without lifting most of it, just pull it along behind you.
Not sure how big an area you are planning. It would help if you used the Google Area Calculator
https://www.daftlogic.com/projects-google-maps-area-calculator-tool.htm to define the area so those who might have an opinion can see what they are dealing with.
Pounding T-posts can be pretty hard on the body unless you have really nice rock free ground. Not sure what it would cost to rent a power pounder and even those have a certain physical impact given they are heavy. Quick search found a rentable PD-55 and it WEIGHS 55 pounds. There might be others that are lighter. I know NOTHING about these things but: How one gets that up on top of a T-post, even by putting it on then tilting, is beyond me. The generic manual one I bought at TSC weighs 17 pounds and that seems heavy enough to me when I am messing with it over shoulder height.
Yes there is existing fence on one side but still! 
