Mass Effect 2 should really have more than one guide because there are things that I would do differently depending on who I was planning on romancing in this game, if anyone at all. I think I will explain this as I go along, but there are areas where there are multiple orders of missions available to you.
I have tried to keep this as spoiler free as possible. I have also split the game into three acts, as in my opinion it's the only game of the trilogy that fits this.
Some tips:
Don't buy fish right away: Speak to Kelly as often as you can and be a bit flirty even if you have no intentions of pursuing this. Eventually you will have a dialogue option along the lines of "You do care!". Invite Kelly for dinner. When you speak to her afterwards, she'll offer to feed the fish for you! At that point, buy all the fish you want! (This also has an impact on the next game.)
Kelly is also good for telling you when the loyalty missions unlock for your team mates so check in with her often. Joker has many quips after every recruitment and a lot of fun dialogue in what I would refer to as act one.
Scanning planets: You will have enough elements if you scan the planets that are marked as Rich until they switch to Moderate. Sometimes they will also unlock something you can land at. These never have unique dialogue so, if given the opportunity, take whoever you want.
When you end up back in the Normandy speak to everyone all the time especially if you have just recruited someone. There's so much more dialogue than in ME1 and oh boy it's wonderful. If they have an option for [NORMANDY UPGRADES] ask them. Should you have the resources you will be able to upgrade straight away but if you don't you can upgrade later on in the tech lab.
If you're looking for character builds, check out this reddit post. You no longer have to worry about putting points in Charm or Intimidate this time; your actions in game give you Paragon or Renegade points. Very early on you will learn about the addition of quick time events too. Nothing actively hinges on these in this game.
PROLOGUE
The best opening to a video game that has happened ever. You already see the choices you made in the last game having an effect.
ACT ONE
FREEDOMS PROGRESS
Once complete, and you are finally connected with the best mode of transport to ever exist, talk to everyone.
DOCK AT OMEGA
RECRUIT THE VETERAN
Speak to the first person you run into.
Get more information from Aria, taking EDI's advice.
RECRUIT ARCHANGEL - Zaeed and Miranda.*
*You're right there and Archangel is my favourite so my personal choice is to recruit him here. Zaeed has dialogue with the Blue Suns leader but someone else has dialogue with the Blood pack that you haven't recruited yet, so I have included an optional spot for this mission.
There's a data pad near the Eclipse leader you can turn in later for extra XP.
RECRUIT THE PROFESSOR - Archangel has unique dialogue if you have him available.
OMEGA'S SYSTEM - Scan the system but nothing else in the cluster. Buy fuel and probes.
DOCK BACK AT OMEGA
Walk around and talk to people.
You should unlock some new missions and lore.
You may meet some familiar faces on the walk around.
A lot of missions unlock store discounts, so don't buy anything until your discounts are applied.
GO TO THE CITADEL You can really take anyone, there's occasionally fun dialogue that triggers.
RECRUIT THE MASTER THIEF
Go to see Udina/Anderson.
There is a quarian speaking to a C-Sec officer and a volus, don't interact with them just yet.
Speak to every shop assistant before buying anything.
If you buy something for the engineers now, stop including them on your rounds when you speak to your crew on the Normandy.
EAGLE NEBULA - SCAN PLANETS
RECRUIT THE WARLORD - Archangel (if available) and Mordin.
[*Optional place for RECRUIT ARCHANGEL - Zaeed and Grunt]
HOURGLASS NEBULA - SCAN PLANETS
RECRUIT THE CONVICT - Miranda and Grunt.
HORIZON - Archangel and Miranda.
GO TO FAR RIM - SCAN EVERYTHING (You might need to stop somewhere to buy fuel and probes.)
RECRUIT TALI - I like the banter that Archangel and Kasumi have for this mission
Talk to everyone on the Normandy including Daniels and Donnelly now that Tali is here.
GO TO THE CRESCENT NEBULA - SCAN EVERYTHING
DOCK AT ILLIUM - Archangel and Tali.
There are multiple call-backs to previous decisions from the first game on Illium.
You can get discounts for most shops here as well, so don't buy anything until you've had a good look around.
Speak to Liara. She will have a task for you.
Fun fact about me - Illium is my favourite place in the entirely of the Mass Effect series. I love how it pulls from the previous game, and how it puts in place some tidbits for the future, if you're paying attention.
You might run into an old friend at the bar.
RECRUIT THE ASSASSIN - Archangel and Tali.
DOCK AT ILLIUM - Tali and Anyone.
You might have some missions to turn in so walk around a little more.
There might be another interaction at the bar.
RECRUIT THE JUSTICAR - Archangel and Thane.
SPEAK TO THE ILLUSIVE MAN
THE COLLECTOR BASE - Everyone has a good amount of dialogue and it's an important mission so take who you like.
Back on the Normandy and that should be all but one person recruited. Some characters loyalty missions will already be available to you and some will unlock during this period. You should start thinking about who your Shepard might want to romance this time around. Male Shepard has Tali as a viable option and if she is your best girl then do not leave her loyalty mission as late as I do. I have included a spot where you could complete Tali's mission should you so wish**. While it is still possible to romance her during the miniscule opening I give you, you get more romance dialogue if you secure the quarian earlier. That said, the exclusive dialogue you get if you wait blew me away the first time I heard it.
ACT 2
SCAN THE CLUSTER YOU END UP IN AFTER THE COLLECTOR BASE
FIREWALKER: ROSALIE
Marked on the Galaxy Map.
Scan the systems first, then land at the planet.
Once you have completed this mission other Firewalker missions will appear on the map.
Complete them all, it doesn't matter what order and it also doesn't matter who you take.
GO TO KROGAN DMC - SCAN EVERYTHING
DOCK AT TUCHANKA - Garrus and Grunt.
Speak to the chief.
There's some upgrades and missions you can pick up.
Eventually head over to the Shaman.
HELP GRUNT - Grunt (mandatory) and anyone.
HELP MORDIN - Mordin (mandatory) and Garrus who has a line referenced in a future scene.
You might need to nip back to Tuchanka to hand in some missions, but you're pretty much good to move on once Grunt and Mordin's loyalty missions are complete.
Any time you head to a new cluster going forwards, make sure you scan every planet and stop to harvest when they are rich in materials.
DOCK AT OMEGA - Samara and anyone.
There will be at least one more mission to take on Omega.
HELP SAMARA - Samara (mandatory) and anyone.
Needless to say, your actions in the loyalty missions have an impact on the whole of the game, but this one is a really big impact.
HELP JACOB - Jacob (mandatory) and Mordin/anyone (it's not a huge bit of dialogue from Mordin.)
SCAN EVERYTHING IN THE "HELP TALI" SYSTEM BUT DO NOT COMPLETE THE MISSION [**Optional spot to complete HELP TALI mission if this is your first playthrough and your male Shepard has his heart set on her.]
DOCK AT THE CITADEL - Garrus and Tali
Walk around the citadel, there might be some more stuff to buy.
Speak to the quarian with the C-Sec officer.
You will inevitably start a mission with those two in toe, so...
HELP GARRUS - Garrus (mandatory) and anyone.
GO BACK TO THE NORMANDY
Make sure you're still talking to everyone. If you haven't done their loyalty missions you'll won't get too much out of them but the ones you have will have a lot more to say.
DOCK AT THE CITADEL - Thane and Garrus
HELP THANE - Thane (mandatory) and anyone.
HELP KASUMI - Just you and Kasumi.
HELP ZAEED - Zaeed (mandatory) and Garrus/anyone (this is only thematic because of the two character's similarities, you can take anyone you want, I just really like how this fits.)
HELP JACK - Jack (mandatory) and Miranda
[**Optional place for HELP TALI - Tali (locked in) and anyone]
SCAN THE SHRIKE ABYSSAL
DOCK AT ILLIUM - Miranda and anyone.
HELP MIRANDA - Miranda (mandatory) and anyone.
DOCK AT ILLIUM - Garrus and Tali
Talk to Liara about the Shadow broker. There will be more of a mission, which opens into a full DLC, and it's really very good.
Take Garrus and Tali to her apartment.
Take Tali in the car.
Switch Tali for Garrus after dealing with Vasir.
There is so much to look at and do once you have finished here, so take a look around.
Okay, so we're getting towards the sharp end here. There might be a few left over missions scattered across the map, so complete everything that is marked with the exception of "Rescue Dr Kenson", "Explore the Normandy Crash Site", or "Project Overlord".
Once you've completed everything bar those three head back to see Liara as there might be some more things available to you.
PROJECT OVERLORD - No one has lines for this, so take anyone. Thematically, Miranda works.
This is a huge, multi-faceted DLC which has an impact on something in the narrative going forwards.
It's a little squeamish inducing, be prepared for some weird eye stuff.
EXPLORE THE NORMANDY CRASH SITE - Solo mission.
ACT 3
We're very much in the end game now.
Go back and see Liara again, there might be some more things you can pick up. Also check that you have completed as many upgrades as you have available on the ship and if you have 300k total minerals remaining you will have a nice bonus in ME3.
ACQUIRE REAPER IFF - Tali and Samara.
Speak to people when you're back on the Normandy. Do no other missions. Do not scan a planet.
HELP TALI - Tali (locked in) and your newest companion. The dialogue here is absolutely brilliant with them.
HELP [REDACTED] - [REDACTED] (locked in) and anyone.
Okay, things now happen and I am not going to spoil it. Do no other missions or visit anywhere other than your destination. It's final mission time.
Take the Omega Relay. Secure that Romance BB!
I am very much of the opinion that the choices that you make at the end of Mass Effect 2 are a rite of passage in video gaming. However, I know some of us love hard and hate losing, so I have included a guide for the suicide mission here.
Go back to Liara, there will be extra bits of info on the dossiers for pretty much every crewmember to read.
Finally, rescue Dr Kenson. This mission is huge and has implications on ME3, but should really be ran after the suicide mission.
This has no impact on the game, but if you did romance someone, you will now have the option to invite them to your room. This has no impact on ME3 but I didn't realise that you could until my third playthrough so this is my gift to you.
On to Mass Effect 3!