I have recently bought 3 of these ottomans (2 are the same size and 1 is a bit smaller) thinking I would paint and reupholster them. They are so ghastly as-is but they were cheap. I love the bold, mid-century graphic look and I have these 2 fabrics picked out [pics of fabric and living room after the jump].
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The fabric should ideally be upholstery weight. Lighter fabrics will not last as long, especially on an ottoman, which can take a beating from shoes.
As for the choice of color and pattern, both of the fabrics you selected will work beautifully with your zesty green color scheme. The yellow will add pop whereas the green will be more restful.
Please send in pictures when you're done!