Trying to get into this series has given me a serious headache. Need help from anyone who knows the

Will add Bring Down the Sky for ME1 (should also be free). Playing it makes a few things in 2 and 3 make a bit more sense.

Also, you can play offline on PC.

I don't have consoles so I can't say anything much here.

If you need ONLY one DLC, I would suggest Leviathan DLC as it ties up Reaper's origin and this is the area where the trilogy is sorely lacking.

Bring Down the Sky and Arrival added up to Batarian lore. I thought it gives layers to Shepard's origin story (Mindoir, Torfan and Blitz). And I prefer Arrival being the reason why Shepard was incarcerated in ME3.

ME2's Overlord and ME3's Omega DLC added more to Cerberus narrative into the trilogy. Citadel DLC gives closure to ME Foundation series but half of it was fanservice which almost everyone like.

DLC companions is fun to have but quite optional in entirety.

If you're a fan of Liara, Lair of the Shadow Broker DLC is a must and its probably the only bright moment in the trilogy that involves her.

As for the rest, weapon DLC can be quite necessary especially in higher difficulty. I hate how Mattock isn't in ME2 base game. In ME3, I couldn't live without my darling Black Widow X.

Appearance DLC is largely optional too and ME2 have a lot of them. I prefer Miranda in armor.

Mass Effect's Bring Down The Sky D.L.C is well worth playing as whatever you do in that mission comes back to you in ME3.
The only other D.L.C for the original game is not that great IMO, and you should only get it if you're wanting all the achievements.

Mass Effect 2 has some great D.L.C.

I think you should recruit Zaeed and Kazumi immediately because Zaeed's loyalty power is very useful.
I personally like to leave Kazumi's mission until later as it breaks the game up a bit and I think her loyalty mission itself is very cool.
You can pick up a nice gun in Kazumi's mission though so depending on what class you're playing as you might want to do that mission sooner just for that reason.

Normandy Crash Site is worth getting. It's not much of a mission really but if you've played the original game then you'll definitely want to experience this short quest.

I personally love the Firewalker missions as they make the game feel less like you're just going from place to place recruiting people. I like to play them periodically through the game to mix things up a bit. I think that ME2 felt a little less epic as the original as you didn't get to control any vehicles and so the levels themselves felt much smaller and it could get a little repetitive and almost feel like a corridor shooter at times.
The Firewalker missions may not feel as epic as landing on planets and exploring them like in the original but I enjoy those missions all the same.

Overlord is one of my favourite ME D.L.Cs. I usually play this mission after I have started on my second round of recruiting people.
It has a great story to it and you can use the Hammerhead if you didn't get the Firewalker D.L.C. It's also pretty dark in content and you have another difficult choice to make in it.

The Lair of the Shadow Broker is another excellent piece of ME2 D.L.C.
Brilliant action sequences and how it ends is pretty cool.
You can play this D.L.C. at any time I think but I like to wait after I've recruited Samara and done a couple of quests on Illium before starting it.
After completion of this D.L.C. you get some cool stuff so some people I know like to do it early but others leave it until later. I even know some people who wait until they've completed the game to start it but it's up to you.

The Arrival D.L.C. for ME2 should be completed after you've completed ME2 IMO. It kind of acts as a bridge between 2 & 3 so IMO it makes sense to play it then.

Mass Effect 3 also has some amazing D.L.C.

The From Ashes D.L.C. is another of my favourites as it adds a unique team member and also has some wonderful story to it. You cant use the character you get from completeting this D.L.C. though until after you've done a certain mission early in the game, Priority: Sur'Kesh I think? But you do get a cool weapon that you can use right away so it's up to you when you want to start it.

The Omega D.L.C. I like to play after the Citadel Coup as for me it makes sense to do it then but again it's up to you.

The Leviathan D.L.C. is absolutely epic. I think it should be done after Priorty: Thessia & Prority: Horizon.

The Citadel D.L.C. I always leave until the very end, the point of no return in the game, after all side-missions have been completed.
There is 2 parts to this D.L.C. though, so do the first part to open up the new hub area and leave the actual party until you've completed all mission for the characters you want at the party, it's one of the greatest moments in the entire series IMO.

Those are the main parts you'll want to go through in order the experience the trilogy as a whole IMO. There are other D.L.Cs available but these are minor things like alternate costumes and additional weapons, nothing major really.

I was lucky to get all the ME2 & 3 D.L.C when it was on sale on Xbox Live. Think I paid £20-25 in total. Might have been a little less than that I cant remember.

I liked Miranda's alternate costume after she's loyal, the black catsuit. But the white original one looked a bit silly.

Moved to ME General as topic was not character/romance related.

As to the topic itself, have you tried the ME Wiki, OP?

masseffect.wikia.com/wiki/Downloadable_Content

It lists all the DLC and how to get them and where they're bundled.

Now my thoughts on the matter.

ME1- Never played any DLC, don't know how crucial it is. I was considering getting some recently, but I already started a new playthrough so screw it. From what I understand Bring Down the Sky is about some Batarian shenanigans, which may be worth it since you don't see Batarians in ME otherwise (to my knowledge). Apparently it's also free so maybe I will see if I can get it.

ME2- the most important story DLCs are Lair of the Shadow Broker and Arrival. They explain how Liara becomes the Shadow Broker and why Shepard had to go full retard in lockup before the war, respectively (because he stopped the Reaprs from arriving 6 months early). Then you have the companion DLCs Stolen Memory (Kasumi) and Price of Revenge (Zaeed). Zaeed you pretty much get for free at this point but Kasumi is totally worth it, for story, for gameplay, for everything. The other optional story DLC is Overlord, a nice little expansion on Cerberus and the geth. It does factor into ME3 (Grissom Academy) so it's worth it (plus it has more sections for the Hammerhead, which is always fun). Otherwise Firewalker is pretty much just Hammerhead missions but you get a cool Prothean Sphere at the end of it and Normandy crash site is a nice but not crucial addon that's exactly what it says on the tin- you get to explore the crashsite and have some flashbacks to the SR1. The rest is just flavor, armor and weapons, feel free to read up on them and decide what you want.

ME3- there's only four SP DLCs and most people have summed them up pretty well. I'd highly recommend From Ashes (Javik), even over Leviathan. Javik actually provides a new perspective on something we took for granted since Day 1 of the series. Leviathan on the other hand, while it has a cool atmosphere merely expands the holokid's nonsense, it doesn't actually provide new information. Plus one squadmate that affects the whole game and like Kasumi gives you a powerful ally and a weapon vs a single contained story that doesn't show up again outside of EMS numbers and one off hand mention at the ending. As for Omega, I'll add that it felt like a different game (still in the ME series) and I found that to be a very good thing.

I don't really have anything else to add here, other than if you are loving or enjoying your run of Mass Effect so far, then most of the single player DLC's are really worth giving a go.

Mass Effect doesn't just have some excellent DLC, some are arguably examples of the best DLC gaming has to offer. Lair of the Shadow Broker is particularly popular and acclaimed, but all are good, with some obviously being better than others.

It would feel amiss not to give them a go.

For me ones like Zaeed, Kasumi and From Ashes are essential as it's not Mass Effect without Zaeed, Kasumi and Javik in it.

Citadel is also cheesy fan service, but that is what works so well in its favour. It's my personal favourite, and one of the best DLC's I have come across. More so than Shadow Broker, simply for all the wonderful character moments, fun and substantial campaign, and the fun of a whole new apartment and Citadel hub area to explore and get lost in.