What's the typical timeline and cost for sponsoring an H-1B vs. EB-3 vs. other visa categories?

Just to be clear, the H-1B is a nonimmigrant visa and the EB-3 is a green card category so they're no comparable. The costs will depend on the legal fees (which run anywhere from $2,500 to $5,000 with most lawyers charging something in between), the size of the company, and whether premium processing is used. For an H-1B, expect total costs of anywhere from about $5,000 to $10,000.