We have a domain and now we need to setup an online store. Which is better for search engines and for people (easy to remember, etc.) - a directory (site.com/shop/) or a subdomain (shop.site.com)?
In my opinion a sub-domain is better to remember, but normally to this cases we use a directory.
You could use both, and just redirect to one of them. Like, if you go for shop.site.com put a redirect from site.com/shop/.
Personally i prefer to use a subdomain because it "feels" cleaner and easier to remember, but i am not sure what search engines think is the best (if they actually think one is better than another)!
Subdomain is the best option. Easy to remember, well organised (regarding file structure), and has no disadvantages regarding SEO (many multinational companies use it)
I personally like paths much better. Also, I'm quite sure that normal people have become used to the "www.something.tld" pattern - it is the usual way of communicating a web address in everyday life. I would bet that the majority of people would not know what a subdomain is, or how to type it into a browser. The organizing argument doesn't count in my opinion, as any kind of file structure can be achieved with directories and subdomains alike (at least in Apache).
store.site.com is a MUCH better solution.
Generally regular users don't CARE about your URL, they just type in "site" into Google.
Then they click.
As long as your store has a prominent place on your site, it won't be a problem.
Apple does this very well:
A subdomain also keeps your "sales" apart from your "content" which different avenues in most businesses.