When you say that "people" have suggested that you have both his front legs amputated, what people do you mean?
You may have a hard time finding a vet that would do that sort of surgery for you. Many will just refuse.
My concern with having both the front legs removed is about his digestion. A three legged animal still stands upright enough that its not a problem, but without any front legs, the front end will be considerably lower than the back end, causing digestion to have to work against gravity, where his body is designed for gravity to aid digestion.
I would worry that as this goat gets older and begins eating "grown up" food, he will not be able to digest as well, and would end up with some serious bloat or at best, some serious constipation. Not to mention the constant strain on his lungs from having all that downward pressure on them. I know a two legged cat who lives on antibiotics from the problems that she has..........her legs were torn off my a dog. However, this cat is a happy cat, lol. Her owner did the right thing to let her live, but this is a cat that is VERY pleased to live out it's life indoors and away from other critters. Cats are just not as social as a goat.
I'm not saying that you need to put him down.......thats a choice that you'll have to make on your own.
I agree with all the questions that have been place before you, such as "are you able to lug a 100 pound goat around" etc in Sunny's post, but I'd like to add a few of my own.
What are you going to do to meet his social needs? He is a goat and will want to be with other goats. How will you handle it when he starts crying to be outside in the pasture and in a herd?
Are financially prepared to take care of the higher vet bills that come with having a severely disabled animal? Without the wheelchair, with or without the legs, he will probably have digestion issues, but if he stays in the wheelchair, he will develop some pressure sores from the constant pressure. AND, with him being so young and having to grow with this disability, the constant pressure on the front end (even with his legs still attached) will deform and cause growth issues. Bones are designed to hold pressure at a specific point. Also, the lack of movement from the front end will cause muscle atrophy in his chest wall, leaving him more susceptible to respiratory problems.
It just wont be a get him a wheelchair and live happily ever after type situation. It will be a large financial burden for you, an even bigger physical burden for both you AND him, and, BOTH of you need to be able to handle the mental burden as well. Maybe you are ready for the physical and mental burden.......make sure that he is and that you are sure that he still will be a year from now. Right now, he is a youngster, curious and easily distracted from hardship, but he may very well end up frustrated and miserable a year from now.
There is a lot to think about here, but it is this little goat that will carry the biggest burden. Please be confident that he can handle it. If you are not positive that he can, the kindest thing to do would be to give him lots of loving and then euth him.
But, if he can handle it, then go for it. If he could survive with the legs still attached, I'd leave them. He's got so much to contend with already, I wouldnt want to add a massive surgery to the mix, but, thats just my opinion worth about as much as the paper its written on.
Of course, there is one other burden that would come with this.....we'll need photo updates of his progression! He sounds like a little booger, jumping from chair to couch, lol.