The Brother machines at Walmart are not bad little machines when used as intended. I bought a CS1000 and loved it. They are made for light duty use like piecing and small quilting projects, light weight clothing and crafts. They will not handle many stuffed animals. They are not built for it. I'm not saying they won't sew them - I'm saying they won't sew very many of them.
A 60's vintage Singer machine is built like a tank and will handle stuffed animals with no trouble. I know a lady selling off her sewing machine collection if you want to go vintage. She has a Singer 503, 500 and a 600 for sale for very reasonable prices if you would want to go that route.