Ditto what everybody else has said about the fencing. My 28 year old mare will literally stay inside anything I put her in, hot or not.
As far as the goats go, I would definitely research breeds and get in touch with a goat rescue/breeder with retiring does. Definitely get an adult[s]. I have two goats myself, a 1.5 year old Alpine/LaMancha cross [40inches tall] and a 10 yer old Angora doe [30in].
The Angora [I got her because she was being retired from breeding] is pretty typical for what I've heard her breed is like - you couldn't force her over a fence that's taller than 2.5ft. She's the EASIEST critter evvvver, as well as being super laid back and quite gentle. Her only downfall is the twice-yearly shearing. It's not hard at all to do yourself at home, but it does demand time, some energy, and attention. I would really recommend looking into Angora crosses [sometimes you can find an Angora cross with the Angora personality and a shedding coat - like some LaMancha/Angora crosses, for instance. LaManchas are another breed that's supposed to be nice.].
My Alpine/LaMancha [wether, he was gonna be dinner...but I got him instead. haha] seems to be heavily influenced by his Alpine side - very active, social, and dominant as all get out. He's always running, hopping, escaping, you name it.
Just today I was trying to clean the barn and was placing empty feed bags in trash bags, then tying the bags closed as they were filled - I left them alone for 5 minutes, without thinking to tie Atti up, and came back to find that he had untied the trash bags and was throwing the contents EVERYWHERE around the barn. It was really funny [thought about murdering him for a second though, let's be honest], but definitely something my Angora would never dream of doing. While he is a huge troublemaker, the Alpine cross is for sure a load of fun - I've taught him many 'tricks' that you might teach a dog and he LOVES to come on hikes with me. He's basically my goat-dog. My troublemaking goat-dog.
And, for the record, he acts like a 4ft fence is absolutely nothing to climb or lithely hop over. None of my fences are hot, just high tensile wire or wood/pallet, and really none of them of them have stymied him. The pallet fencing has proved to be more tricky for him [I made absolutely sure there were no footholds it the way I put it up] but I imagine that, if pushed, he'd figure out a way over. He'd probably respect electric, hopefully, though! haha
Fabio - 13 year old Arabian/Lipizzan gelding
Hazel - 14 year old Angora goat
Atticus - 4 year old LaMancha/Alpine cross goat
Rest peacefully, Lacey.