Where should I buy iphone 5s?

Should i buy it online on apple site or go to an actual shop?

I think you should purchase it in an actual shop
Because you can purchase other accessories as well

I have worked as a Customer Service Rep for a major wireless provider in the US I always told my customers it is best to at least go in to a store somewhere and handle the phone that they are thinking about purchasing, play with it, etc, before they hand over their cash for it. If you are already certain that the iPhone 5S is the phone for you then it just comes down to price, convenience and level of service you want during the purchase process. With the iPhone, pricing is nearly identical across all retailers.So, ask yourself do you want the convenience of ordering online & having the phone shipped to your door? But then you are pretty much on your own for setup and activation. Or would you prefer to go to a store, wait in line for who-knows-how-long, but be able to walk out with a working phone? Hope this was helpful!

Either or. Same result either way.

Nowadays though with them in short supply I'd order online. At the very least it guarantees you would get one, unless you don't mind checking the stores ever so often, which may get you one faster should they have enough stock at the time.