this blog usually has good info:
http://effortlessanthropologie.blogspot.com/?m=1
Anthro sometimes has extra 20-30% off sale items, and more rarely a small discount on regular priced ones. Nothing like gap or br though. Stuff gets marked down on Mondays if you want to check then. First markdown is usually 50%! The cycle is unpredictable though. Some things never go on sale. (The blog I linked usually lists new sale items.). They'll do a 14-d price adjustment so it's worth checking after the fact.
Re:shipping. If you order in the store, shipping is free. They link it to your online account and it ships to your house so there's no difference except you paid in the store.
I prefer to try in person anyway... The sizing is inconsistent (they have many house brands, all with diff sizing, and other brands as well) and so is quality. I live within walking distance of the store though! (Dangerous...)
ETA: store stock varies a lot though. Check on the website if it's even I your store first. (I think they can still order it for you if its not there but it doesn't help if you want to try it on...)