Following parts 1 - 3 is definitely the way to start. I haven’t checked the rest of the guide for order of agents but it definitely looks good, especially for reference. Back when I did Cosmos years ago, I basically tried to do all lv 1 agents first, then lv 2, next lv 3, ending with lv 4.
Course I found out that I couldn’t do that with some of the Factions, especially with the Amarr Cosmos Agents. They have a lot of agents chained together which need to be done in a specific order. When working them, agents and mission completion will jump around a lot.
I helped write this guide which worked great to complete all of the Amarr Cosmos Agents:
http://web.archive.org/web/20160225230248/https://wiki.eveonline.com/en/wiki/Amarr_Cosmos_(Guide)
Anyway, according to my notes the other Factions also have a few Cosmos Agents that are chained together:
Gallente Federation
Barmalie System - The Ebony Tower
Pandon Ardillan - Level 2
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Audaerne System - Natura Seminary
Preaux Gallot - Level 2
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Barmalie System - The Ebony Tower
Ystvia Lamuette - Level 2
Fluekele System - Contested Gallente Roden Shipyard
Nilla Elermare - Level 3
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Fluekele System - Central Administration
Aminn Flosin - Level 3
Caldari State
Colelie System - Survey Station
Aakeo Oshaima - Level 2
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Fluekele System - Central Administration
Veko Tallaja - Level 2
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Jolia System - Grand Future Information Center
Gara Kort - Level 4
Otomainen System - Rush Town Ruins
Akira Helkelen - Level 3
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Otitoh System - The Diamond Ace Den
Ryoke Aura - Level 3
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Otomainen System - Foul Creek Ranch
Goru Nikainen - Level 3
Minmatar Republic
Barkrik System - The Carnival
Dagras Kutill - Level 3 (Buy mission objective items to complete missions 2 of 3 and 3 of 3 for access to next agent)
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Barkrik System - The Carnival
Rozor Mothrus - Level 3
Thukker Tribe
Augnais System - Nickel & Dime Store
Pattok Nortul - Level 1
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Augnais System - Nickel & Dime Store
Iliere Angetyn - Level 2
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Deltole System - Municipal Junkyard
Krester Rupptofs - Level 3
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Parchanier System - Latent Transmitter
Drusk Amakkit - Level 3
I also helped compile this list of Cosmos Agent locations:
http://web.archive.org/web/20160225230111/https://wiki.eveonline.com/en/wiki/COSMOS_constellation
Before running each Factions Cosmos, I’d research various guides to see which items were needed before actually talking to the Agents. That gave me time to gather the items first which allowed me to easily complete each mission in their series within the bonus time.
Unfortunately most of the guides I used back then have now become inactive, however some can still be accessed through Internet Archive.