I've made a flowchart ordering the events whose relative order we know. Explanation of the ordering follows.
The canon version of events is the more straightforward one, and was recently clarified further by the series Tales of the Jedi. The only outright contradiction is in the Ultimate Star Wars reference book, which explicitly places Sifo-Dyas' clone order and death after TPM (page 190, Kamino), but multiple recent and more authoritative sources disagree.
- 42 BBY: Dooku leaves the Jedi Order, keeping his lightsaber (The Star Wars Book, Dooku: Jedi Lost). During this time, he remains on good terms with the Jedi, and occasionally visits the Temple. Some still refer to him as "Master" out of respect. (Tales of the Jedi Episode 4: The Sith Lord)
- Dooku first learns of Sidious' Sith identity / Dooku becomes Sidious' apprentice (Rise of the Separatists sourcebook). Before TPM, Dooku seems to have been sort of an informal apprentice of Sidious's, and followed his orders, though wasn't yet fully committed to the Sith. (Tales of the Jedi Episode 4: The Sith Lord)
- 33 BBY: Sifo-Dyas orders the clone army on Kamino. (Complete Visual Dictionary, Timelines)
- 32 BBY: Sifo-Dyas disappears/dies on Oba Diah. (The Clone Wars: The Lost One, Timelines)
- 32 BBY: The Phantom Menace. TPM happens after Sifo-Dyas' death, since he was on a mission for Chancellor Valorum, who was no longer Chancellor by the end of TPM. During the events of The Phantom Menace, Dooku uses Sifo-Dyas's identity to erase Kamino from the archives. Following Qui-Gon's death, he joins the Sith more officially. (Tales of the Jedi Episode 4: The Sith Lord)
- 32 BBY: 'Tyrannus' 'takes over' from Sifo-Dyas as the Kaminoans' client following the events of The Phantom Menace. (Ultimate Star Wars, Timelines)
- 32 BBY: Jango Fett is recruited on the moons of Bogden (Age of Republic: Jango Fett). This takes place post-TPM. (Ultimate Star Wars, Timelines)
- 32 BBY: The Kaminoans begin production of the clone troopers. (Timelines)
Much of the order is the same, except in Legends, Dooku left the Jedi Order after TPM, which creates some inconsistencies.
Dooku first learns of Sidious' Sith identity
This apparently happened first, since Dooku was apparently training under Sidious at the time Sifo-Dyas made the clone order. This creates an inconsistency given that Darth Plagueis says that Sidious hadn't revealed himself by the end of The Phantom Menace, although Sidious and Dooku had had a working relationship by then.
Dooku becomes Sidious' apprentice
Dooku was apparently training under Sidious at this point, since according to Jedi vs. Sith: The Essential Guide to the Force, killing Sifo-Dyas was required for his promotion to Sith Lord.
Note that this is a fairly large inconsistency, since Darth Plagueis and other sources strongly imply that he hadn't turned until later. The Essential Guide to the Force in particular seems to have assumed that the Tyranus/Sifo-Dyas events took place post-TPM, not least because of the Rule of Two, but this assumption was apparently later retconned.
Sifo-Dyas orders the clone army on Kamino
Darth Plagueis and Darth Sidious arranged for Sifo-Dyas to fund the creation of the clone army, using funds provided by Plagueis's company Damask Holdings. This is described in Darth Plagueis and appears to uncontroversially take place before TPM.
Sifo-Dyas disappears/dies on Oba Diah
This apparently happened before The Phantom Menace, since Chancellor Valorum's aide, Silman, was present at the time, according to the TCW episode The Lost One, and Chancellor Valorum has been replaced by the end of TPM. Sifo-Dyas was murdered by Count Dooku in all versions of his story. This happened relatively soon after ordering the clone army.
Note that TCW is the first mention of Sifo-Dyas being killed by Dooku pre-TPM; without this detail, there would be very little inconsistency.
The Phantom Menace
Valorum replaced by Palpatine as Chancellor. Palpatine kills Plagueis during the events of the film, according to Darth Plagueis. Qui-Gon is killed and Darth Maul is believed dead.
Setting up the army (order unclear)
a. Dooku leaves the Jedi Order
Officially, his leaving was due in part to his dissatisfaction with the Jedi's actions at the Battle of Galidraan, which definitely took place before TPM (variously in 44 BBY and 34 BBY in Legends), but ultimately he only left after Qui-Gon died in TPM.
However, since he'd apparently fallen to the dark side at this point, this can be assumed to be a cover story. In any case, he could only have erased Kamino from the archives while still a Jedi (according to Attack of the Clones), so his leaving would have had to have happened after he was at least aware of the cloning plot.
b. 'Tyrannus' 'takes over' from Sifo-Dyas as the Kaminoans' client
Probably happened before hiring Jango Fett, but it's unclear.
c. Jango Fett is recruited on the moons of Bogden
Shown in Bounty Hunter.
The Kaminoans begin production on the clone troopers
Presumably this happened last, since the genetic template would need to have been selected, and Dooku would need to be able to set things up with the Kaminoans.