First I did the Caldari Data Center missions. When I started I only had Connections III and I needed Connections IV for modified standings to access the last 3 agents. I had 4.88 with Home Guard but needed 5.0+, so I waited a couple days for Connections IV to train first.
I could have just done some courier missions for Home Guard instead of waiting but I wanted to see exactly what my standings and broker fees would be after doing nothing but the Caldari Data Center missions.
With Broker Relations V that's standings of 2.21 with Caldari State and 1.52 with Caldari Navy, good for a 0.57% broker fee (0.18 less than with 0 standings). Not bad considering all it takes is about 300 million ISK to buy the tags and 10 minutes to do the missions.
Then I did the Amarr Data Center missions which have more missions covering 3 factions, Amarr Empire, Ammatar Mandate and Khanid Kingdom, all of which give derived Caldari State faction too.
Then I ran into some weirdness at the data center in Kudi system. I got stuck on the 6th mission in Kudi (with Timafa Esihiz for blood raider palladium tags) because I only had 2.73 standing with Ministry of War corporation but needed 3.0. I didn't have any problem with Ammatar Fleet standing in Ferira, in fact I had 4.71 with Ammatar Fleet when I got to palladium tags there, way more than the required 3.0.
Consequently I had to grind 9 level 3 distribution missions with Ministry of War before I could finish. Making matters worse, the main Jita trader is my only trader that doesn't fly Prowlers yet (didn't need to since he never flies transport and hadn't even undocked in over a year) so I was forced to buy a wreathe and fly it for an hour.
I hate flying T1 Industrials, they're SO SLOW!
There were 3 Ministry of War level 3 distribution agents in nearby Andrub (5 jumps from Amarr) so at least finding agents to do the grind with wasn't bad.
The first agent gave a mission with a low sec destination which I declined but the other 2 gave all hi sec destinations. I like how they added a warning if you try to undock without moving the cargo into your ship first. That saved me from myself a couple times.
With that finally done, I returned to Kudi to turn in the rest of my Blood Raider tags. And it still wouldn't let me turn them in! WTH?
So I did a tenth mission to bump my MoW standing to 3.03 just in case it actually needs to be over 3.0 and tried again. Still no joy.
My current standings are:
Assuming I get a useful answer to my ticket (one that allows me to do the rest of the Blood Raider tag turn-ins) my standings will go up a bit further yet. I figure I'll wind up somewhere around 3.5 with Caldari State. Then it'll be time for the Caldari Navy grind which I'll pay someone to do for me.
Cost to buy all the necessary tags for Amarr standing (twice as many as for Caldari) was about the same as for the Caldari missions, around 300 million. Time taken to finish the Amarr turnins (the ones I *could finish) was well over an hour, mostly due to the snafu with Ministry of War standings.
Total cost to buy tags for all the Data Center missions with both Caldari and Ammar, about 600 million ISK. Total time about 3 hours but I could easily cut that to less than an hour.
I entered a ticket about the broken Amarr missions a few days ago, it got actioned today but I'm still waiting for an answer.