Possessive, compound nouns or "of" plus noun phrase?

This is an area that often confuses both learners and teachers mainly because sometimes all three options are possible (The company's policy is...; The company policy is...; The policy of then company is...), sometimes only two out of three (Italy's coastline; the coastline of Italy) and sometimes only one (David's car). It's an area that is so complex as to be virtually inexplicable - the best explanation I know of the possessive/of distinction can be found in Quirk et al A Grammar of Comtemporary English (Longman) - see sections 4.97ff, but even that is, in my opinion, open to criticism and they don't deal with the similar use of compound nouns. However, here are some guidelines:

Possessives vs Prepositional Phrases with of

The possessive 's (singular) and s' (plural) will generally be used with personal names and countable nouns denoting people or animals when a relationship of "belonging to" is indicated - eg   John's car / the childrens'  bedroom / my dog's ball:  the underlying propositions are John owns a car; the children possess a bedroom; My dog possesses a ball. This is also true when the "possesssed" item is a family  member or part of the body : John's children, the childrens' legs, the horse's tail

However, where the underlying proposition is a relationship other than "possession", then either the possessive forms or the of construction may be used as long as the head noun is specific :
Lady Gaga's fans / The fans of Lady Gaga
Admiral Nelson's portrait / the portrait of Admiral Nelson
Generic reference must be made, however,  using the of construction:
He's a fan of Lady Gaga / I saw a portrait of Admiral Nelson.

The dual possibility extends to nouns, whether proper or common, describing places and organisations : 
Italy's problems / the problems of Italy
The university's policy / The policy of the university
The European Union's headquarters / the headquarters of the European Union

and what Quirk et al somewhat vaguely describe  as "nouns of special interest to human activity" :
in freedom's name / in the name of freedom
the strike's end / the end of the strike
the game's history / the history of the game
the car's performance / the performance of the car

Quirk et al  also specify other categories where the possessive form is predominant - and combining some of these I would suggest one would be measurement - whether of eg time, distance or value : New Year's Day / A moment's thought / a week's wages / his life's work / his journey's end /  at arm's length / a stone's throw away / your money's worth.

And what about compound nouns?

Compound nouns consist of two juxtaposed words where the first has a classifying function - it describes a quality of the second noun (which is the head of the noun phrase). Here we are only interested in combinations that can be classified as noun + noun. They may be written as one word - holidaymakers, toothpaste; as two words - company policy, university exams;  or with a hyphen - chat-room. Sometimes all three possibilities exist : chatroom, chat room, chat-room.

As I suggested at the beginning, very often there is a choice between the compound and the possessive form and/or the of construction, and often the range of possibilities  will depend on grammatical factors. So :
This is the company's policy / the policy of the company / the company policy - all three constructions are possible. But :
This is a  *company's policy / a policy of the company / a company policy - the possessive construction is not possible when talking about a specific company while the other two are.  
This is explained by the specific vs generic reference distinction mentioned above. But what about:
There was a twenty minutes' delay / a delay of twenty minutes / a twenty-minute delay
Here the distinction is due to the classifying function of the first noun. As it is acting as an adjective, the noun cannot be pluralised.

But do some compound nouns just have to be considered as fixed lexical chunks which will not change regardless of context  - I'd suggest that many  examples are in this category. None of them can be replaced by either of the other two constructions : a stomach bug / a washing machine / a 'flu jab / a bus stop / an egg sandwich / a summer holiday.

For some great teaching ideas...

Gerngross, Puchta and Thornbury, Teaching Grammar Creatively, CUP

(Remember that Amazon often has both new and used copies of the books you want at prices lower than those advertised here. It's always worth checking it out.)