If you have not played Pandemic Legacy, I recommend that you do so before you read this. There are significant portions of this game that will be less fun for you if you know that they are coming. In this post I will be focusing on the characters we played through our journey and why we picked them.
We made a very lucky choice in our starting characters. We picked the Generalist, Scientist, Dispatcher, and Medic. It wasn't lucky because that combination was amazing in the game, though. It was probably a sub-optimal choice actually, but what made it amazing was the first twist; Relationships. These give you great advantages when you play certain characters together, but you can only put them on characters the first time they are played. So none of the starting characters can have them unless you introduce a new character. Because of our starting choices, we were able to replace the Generalist with the Researcher, and give him and the Scientist the Co-Worker advantage. This was amazing since it let the Researcher feed cards to the Scientist from anywhere in the world, which was a huge advantage in many of the games. I think this is one of the big reasons we only lost twice in the whole run of games. And it was only possible because we had chosen not to play the Researcher on the first game.
The Dispatcher is one of my favorite characters, but we fairly quickly replaced her with the Quarantine Specialist for two reasons. First, quarantines are very powerful. They can prevent outbreaks like nothing else. The other reason we switched was to get a Rival relationship going between her and the Scientist, which gave him another way to get the cards he needed to cure. Plus she's military which was VERY useful for most of the game.
We basically played those 4 characters right up until the point that we were required to [HUGE SPOILER] kill one of them off. The Quarantine Specialist had the paramilitary escorts, so she had to GO! There were some points where we considered swapping one of the characters out for the soldier once the infected appeared, but we were pretty lucky in our setups in games and never felt like we really needed someone who could kill all the faded quickly. If we had had a setup with a ton of them, we might have made a switch for that game, though.
When we were required to kill off the specialist, we switched back to the Dispatcher, and stuck with her through the rest of the game. The only other characters we ever considered were the Soldier (as described above) and the Immunologist for the last game we played to vaccinate faster. We did sub in the Immunologist in December and gave him a Family relationship with the Dispatcher for the extra actions, which came in handy.
The Colonel seems weak. He can kill faded, but if the Soldier can get access to grenades, he can do it much better, and so we saved the grenades in case we ever needed them and planned to sub him in if the setup was crazy. We also never really played with roadblocks. They just seemed to limiting except in emergencies. We did pull them out at such times, but never made them permanent.
The operations expert just seems so bad. You rarely want to build anything and if you do, it's just not that difficult to get it done. It's also possible that having the researcher around to push cards around made it easier to live without this character.
The Virologist is strong, but one dimensional. The soldier is probably just as good in the first and probably second game you introduce him, and has a lot more versatility after that.
I hope this gave you some insight into the different characters and why you'd want to play them.