From experience AND many replacements, I would not use the welded wire. The welds simply are not strong enough to with stand time, weather and goat bodies rubbing against it or standing on it. You are better off in the long run going with a field fence with a twisted joint at the squares or even the galvanized panels. You'll also need to have 6 foot T Posts driven 2 feet and spaced every 4 feet for strength and support.
Mini goats can be just as hard on fencing as standards, thats all I have ever had and within 3 years time I spent more money and time replacing the welded wire fencing than what I did on the galvanized goat panels I have for pens now.
This is my second year of having goats, when I got my first girl she was 3 months old and the only pen I had was the dog's pen so I put her in with my 12 year old chow. The two of them loved each other and Onyx my chow protected her. Their pen is attached to the back of my house and is a big square 50' x 50' made of galvanized wire and I have never had a problem with keeping them in. This past winter I lost my dog when her legs went out from under her and that created a very long winter with my girl (Angel), Angel went into a depression over the loss of my dog so when the weather got warmer I went and got another little girl (Chanti) now I have two happy girls. Sorry I got off track there but the area I have for the goats is plenty large enough for them. I am planning on changing the fence and am going to chain link with barbed wire on top because where I live, I have to worry about coyotes.
I bought the goat fencing from TSC. It has knotted joints rather than welded. It's awesome and easy to put up. We attached it to our three rail horse fence. I did our chicken run with the welded wire 3 yrs ago, also attached to 3 rail fence and the welds are already popping. Best to spend a little more and do it right the first time
If you go with the 100 ft of fence it would make a 25' x 25' square pen which would be adequate space for 2 goats. Also, you don't need it to be 6 ft tall, if you go with the 6ft fence you would need at least 7 ft posts and those are harder to get in the ground due to being so tall. The welded wire is pretty cheap and it is a very small gauge of wire, it also doesn't take being stretched very well, the welds are just too weak to handle being stretched as tight as the fence needs to be. If you don't want a huge pen, I would just get either the goat panels or the combination panels (they have smaller squares at the bottom going to bigger squares at the top, they are 16 ft long each and usually 52 inches tall. You would need a post on each end and at least one post in the center to keep the goats from bowing them out.
For wire I would go with the goat fence TSC has, it is 4 ft tall and only requires at least 5 ft posts. The wire is a heavier gauge (12.5 instead of 14) and is the class 1 galvanized to prevent rusting. The only problem with the goat fence is it is a 330 ft roll and VERY heavy. It can be put up with two people, but the roll can be difficult to stand up and move around. It is also very important when putting up a wire fence to use a fence stretcher and stretch it good and tight, otherwise the goats can smash it down, push it up on the bottom and it makes it easier for predators to get in. You can not stretch this fencing tight enough by hand, I just put up two rolls at a rental place and we used the truck attached to a stretcher to get it tight. You also need to use braces in your corners to keep the corners from giving in to the fence. If you have it tight enough you only need the posts spaced every 10 ft. You can also run a string of barbwire at the top to help prevent animals from jumping over it.