2) It seems like a good selection. I can't claim to have read all of Arnold's poems so maybe some gems have been missed out, but all the most well known poems are included: Dover Beach, Empedocles, Thyrsis etc.
1) This edition has no notes. This is a matter of taste but I find some notes, in the Penguin Classics style, to be helpful. Arnold's poetry is so difficult as to make this a real problem, though.