
A Classic Mystery Primer, Part 1: Agatha Christie
First stop, more Agatha Christie!
Christie published over 70 detective novels and short story collections (along with a few plays). My personal preference with Golden Age mysteries is to start at the beginning and read chronologically, but with 70 novels you might want to pick and choose. Miss Marple and Hercule Poirot are the best known of her detectives, but she used at least half a dozen others who might pique a new reader's interest.
Poirot: Symmetry and Logic
Who is the detective?: Poirot was Christie's first detective, and there's a clear comparison between the stories of the little Belgian and his literary predecessor Sherlock Holmes. Although Poirot disdains some of Holmes' evidence-gathering methods (throwing oneself about on the ground in search of cigarette ash is most definitely not Poirot's style), many familiar notes will sound as Poirot's keen observation and logical deduction sees him untangle what to his Watson-equivalent, the good-hearted but mildly comedic Hastings, is a Gordian Knot of mystery.

Where to start: With Christie's very first novel, The Mysterious Affair at Styles, which is a classic English country murder. Another option is The Labours of Hercules, a collection of short stories in which Poirot is challenging himself with particular cases before retirement.
What to skip: A very influential novel, but I'm not a fan of this sort of twist ending: The Murder of Roger Ackroyd.
Miss Marple: Fluffy But Deadly
Who is the detective?: Miss Jane Marple, an elderly resident of St Mary's Mead, devoted to her garden, and the observation of human nature. Christie created Miss Marple because, during a stage adaptation of The Murder of Roger Ackroyd, the narrator's spinster sister was replaced by a young girl character, and so Miss Marple became a deliberate attempt to give a voice to one of the least-heard members of society: elderly women.
If ever there was a mystery series dying to be written, it's Jane Marple's early life. Along with possessing keen intelligence, young Jane attended art courses which apparently involved the study of human cadavers, and she (claims to have) won awards for marksmanship, fencing and equestrianism. Where are the Steampunk Jane Marple novels?

Where to start: The first Marple novel is Murder at the Vicarage and is a solid 'everyone has a motive' story. Another good starting place is The Thirteen Problems, a collection of short stories, or the wonderful juxtaposition of fluffy spinster and jaded millionaire in A Caribbean Mystery.
What to skip: The Mirror Crack'd from Side to Side. One of my main reasons for disliking a book is if it leaves me depressed, and this is definitely one of those.
Tommy and Tuppence: Time Goes By Adventurers

Where to start: The first in this series of four novels and one short story collection is The Secret Adversary.
What to skip: The T&T books are a very distinct set of books. If you liked T&T in the first book, and enjoy the idea of watching two characters mature and change over time, then read on in order. The later books especially are not Christie's strongest, but you do have to give Tuppence points for refusing to be left out when the War Office is only interested in recruiting her husband.
Ariadne Oliver: The Author as Character

Where to start: Ariadne Oliver first appears in a short story (to be found in the collection Parker Pyne Investigates). Her full introduction is in Cards on the Table, a mystery involving around a collection of detecting experts and a collection of suspects. My favourite of her appearances is probably in Dead Man's Folly, where she is a guest at a garden party, and has been asked to write the clues in a scavenger hunt.
What to skip: The Pale Horse, which focuses primarily on a one-off character, Mark
Easterbrook, and involves witches.

For something different, try a couple of the short story collections:
The Mysterious Mr Quin (and two later stories): A mysterious figure who intrigues and impresses social doyen Mr Satterthwaite. These stories combine touches of the supernatural (Quin) and often issues of romance. Rather fun.
Parker Pyne Investigates: Pyne considers himself a 'detective of the heart', and features in a series of mystery short stories which bring about romantic resolutions.
Although best known for her classic mysteries, Christie also turned out quite a few books which would be better classed as thrillers, over-flowing with espionage, master criminals, secret societies and, well, unlikely and overblown plots. Some notable books:
And Then There Were None: Racist poetry and all. It would only take a touch of supernatural to turn this particular book into a forerunner for Halloween and Friday the 13th, as ten people trapped on an island are picked off one by one.

The Man in the Brown Suit: Take one young orphan, longing for adventure. Add an accidental death, a strangled young woman and a mysterious man in a brown suit and you end up in a spanking and romantic tale that ends on an island in Africa. One of my favourites of Christie's adventure tales.
So, we've scratched the surface. Part 2 of the Primer will cover some of the classic detectives not written by Agatha Christie!
Have you read any Christie? Do you agree/disagree with any of her assessments?