The correct order is:
1. Kirk
2. Picard
3. Archer

Sam Well done. You are two thirds correct. LOL

But what about The Sisko??

Kevin I like to think we're both 100% correct since we agree that Kirk is #1!  LOL!!!

Tim I rank Sisko at #5, after Janeway at #4.  I don't believe Paramount really supported DS9 to its fullest.  DS9 could have been a great ST series if they had.  Maybe it was because it was overshadowed by Babylon 5.  Or maybe Paramount had "Star Trek fatigue".

Star Trek Fatique for sure was around Enterprise - the ship, not the car rental agency.

1. Picard
2. Kirk
3. Janeway
4. Archer
5. Sisko

And that is my Mount Rushmore of Starfleet captains

OK, I have two different rankings here: who would be the most fun to serve with, and who I would actually trust with my life.

For fun on the ship or an away mission:

1. Kirk
2. Sisko
3. Picard
4. Pike
5. Janeway

Archer would be near the bottom for me. Too much "we have no idea what this alien virus does, so let's go investigate it personally."

But for the captain most likely to take care of the crew and give me the best odds of surviving the episode:

1. Picard
2. Janeway
3. Sisko
4. Pike
5. Kirk

Kirk would be a blast, no question. But I would absolutely avoid wearing a red uniform anywhere near him.

Come to think of it, I really didn't like Captain Archer at all. He was neither fun nor caring for his crew, lol. I guess that post-9/11 terrorist mentality came through too hard in that show, and it just turned me off. Plus, that whole temporal Cold War storyline was just dumb.

ST:E had so much potential.  I was really looking forward to seeing the exploration of planets/cultures that are featured in later ST series; the Romulan war; and the formation of the UFP.  I 100% agree that the temporal Cold War storyline was dumb and, I believe, killed the series.

The series was killed by Franchise Fatique... but from creative end and fan base.  Sadly the latest stuff isn't catching on... (to me). It's all about ratings, advertising in the end.