For Sisko I think he more tac. Yes he was involve with defiant. But this was after XO of Ship. So it very much possible his involve was that of Project Leader which would not mean he has engineer back ground. Remember the defiant is the first federation warship. Design for fight, such the borg. Make more sence for Tac Officer to lead the project.

Here is how I would put them:

Archer practically got into the game before such heavy divisions were made but I think he leaned more towards Engineering considering his Father's contributions and his own understanding of the technology of his day. In particular he seemed like an Operations Officer.

Kirk was obviously a Tactical Officer, He shoots first and asks questions later.

Picard would most likely be a Science Officer. He is rather sharp, knows his archeology, and seems to have more than a passing familiarity with astrophysics. Apparently he is a very well rounded Sci though.

Riker when he finally got there was more of a Tactical Officer. He seemed to have a very good grasp on Combat Tactics and a notable willingness to use them when needed.

Janeway is a Science Officer. That is not even up for debate if you watch Voyager they flat-out say this.

If we must include the Sisko, which I would rather we did not considering he was only barely the "Captain" of anything, I would place him solidly into the Tactical category but say that as a Tactical Officer he was a pale shadow compared to Kirk in terms of strategy which is rather sad.

The DS9 episode "Homefront" specifies that Sisko is an Engineer. I know that he acts more Tactical Officer, but he is an Engineer. *shrug*

I honestly don't think it's possible to squeeze any of the characters into the STO game system especially not based on the abilites captains have in the game.
It's part of the compromise you have to make when you only put in 3 classes, you have to somehow shoehorn stuff in.
I'm sorry if this offends anyone but I think attmepting decades after the fact to somehow stuff characters from the shows that were, depending on the plot, leaning more towards this proficienicy or the other into the three categories (especially characters like Kirk or Janeway when the script was written by Jeri Taylor since then they both were some kind of universal genuises) will be at best comfusing and at worst lead to endless discussion.
Case in point: Picard ordered the shields frequencies to be rotated in "Best of Both Worlds", would this not also make him an "Engineer"?

No I remember that but thats not what I'm thinking of.

I think it's a mistake to equate Tac with combat or to view Science or Engineering with non-Combat. There's little to confirm this but I'd see Chang as a Science Captain, for example.

Sisko was the one who seemed to recognize the design flaws in ships. His combat strategies were rooted in engineering. He built not only the Defiant but also the Bajoran Light Ship in his spare time. Think back to The Visitor. That all happened because he ran down to Engineering to fix something.

The reality with Trek is that many people have multiple fields of expertise and there are more shades of grey than just three branches.

But aside from planning fleet movements (which in no way correlates with Tac in-game, which represents Security Chiefs more than it does Tactical Officers), the bulk of Sisko's actions in space were those of an engineer. He just had a few points invested in Tactical talents. :-)

(Again... multiclassing would be a sweet feature.)

I think it safe to say in any way what makes a good captain is some knowledge of all three. Or at least to.

To me

Tac = Security, Tactical, Strategic operations officer, Intelligent Officer basically anything to do with Combat

Science = Medical or any of science branch, Exploration etc

Engineer = Engineer, Operation, ie building, maintenance and running tech for Star fleet. This would also be back bone that allows the other to do there functions.

Archer was Engineering, because he was involved in the NX Projects and the Warp 5 Engine.

Kirk was Tactical, remember he served as Tactical Officer on the Faragut (TOS: Obsession). And his time on the Enterprise, he was infamous as a tactical strategist.

Picard was an Archeologist (TNG: The Chase) but later transfered to the Command Branch (TNG: Tapestry) and served as Flight Officer (Conn) on the Stargazer. (So Picard went from Blue Shirt to Red Shirt).

Sisko studied as an Engineer (DS9: Homefront / DS9: The Adversary)

Janeway was a Science Officer (VOY: Shattered / Innocense)

All captains from the various series would have had at least some Tactical proficiency or they wouldn't have been given the ships they were in charge of. Most seemed to havea strong leaning towards either science or engineering though.

I think that Kirk would have been engineering. Engineering seems to be about the practical application of science and I strongly suspect that if you were to check with Bones, Spock, and Scott during the slow times to see who he was helping it would be Scotty. He was just a practical kind of man.

I think that while Science was clearly a strong hobby and side interest that Picard was a man of strategy at heart and Tactical is his real home.

Janeway seems like an even split between Science and Tactical to me. I didn't particularly care for Voyager but her forceful and sometimes cunning attitude is something I don't think you see in the Science oriented mind very much.

Sisko was just awful. I'm guessing that he was a second rate security officer with some Engineer in him who was shifted out to what first seemed like a baby sitting assignment by Starfleet. He was allowed to stick around so that they wouldn't have to admit to the Bajorans that they were just getting a problematic burnout out of their hair. The character solidified their ability to stick around and inflict terrible acting on us for the first three sessions by becoming the message-boy of wormhole aliens.

Archer was almost definitely just an Engineer. He didn't seem very tactically talented. He seemed like one of those people who got their job by being "good enough", popular with the public and possessing the ability to not be a coward when threatened.