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Wether or not your goats will climb (or jump) the chain link depends entirely on the individual goat. Most goat and hog people use electric fencing to keep the animals off (and thus in) the fence. I believe the reccomendation is 6" off the ground to keep them from going under, and another one at shoulder height (the animals shoulder height). I don't know if your pasture would count as grass or browse, but I do know goats will eat nettles, and thistle and such. Goats even prefer feed like that, from what I hear. As for dairy goats (goats used for milk) I reccomend the book "Storey's guide to dairy goats". It's a great, informative book and then you'll know enough information to ask the right questions, or not ask questions if it answers them all for you!
Try joining Backyardherds (BYC sister site, there's a link at the bottom of the page), the people there are very informative.