Just buy the core online pretty much anywhere. The minis online sites where we use to get stuff or amazon at times is a good start. I think pretty much everything is in stock now so prices wont get crazy on the sites like they did for a few expansions thats when amazon has come into play.
then figure out what you like to play and go from there.
I would pick from Stark, Lannister,Baratheon,Targaryen which are in the starter and have expansions for them or coming soon.
Stark doesnt have a expansion based on it but it has a little spread out everywhere which is good and bad.
I would go on the website and the forum to figure out what chapters you need to buy.
I am a big fan of stark,Lannister
expansions(Each one is based on a house but has other cards too)
Kings of sea-GreyJoy house
Lords of Winter has a little of everything but it has a good place for stark
Kings of the storm Baratheon House is a good start
Princes of the sun: Martell house
Queen of the Dragon: I dont have it but its great for Targaryen House and dragon builds from my understanding
Lions of the rock which is not out but will be great for lannister from my understanding.
If you want to play multi player just do Core+chapters and not the expansions they can mess things up. Really the Chapters can mess things up too but not like the expansions can. I would just stick to two player or core.
If you start playing the game with others getting two core sets is a good thing.
For looking at cards the site Boris posted and
http://agot.dbler.com/(it has not been updated in a lot time tho.