I also bought the "Legendary" Edition for ~eight eurobucks and I am right now in the middle of a ME2 play through in my planned trilogy play through, I expect to be finished in a couple weeks.
First thing I noticed is I can not play without a working on line connection, which makes me want to pirate the fucking shit.
But back to the content. I was pleasantly surprised by Mass Effect I, it holds up very well with the little Botox treatment it got in LE. Personally I don't think the combat is clunky at all, maybe basic but not clunky, the most annoying thing is I couldn't get Sheppard to clean all that super glue he has on his armour that keeps him getting stuck on any horizontal surface he approaches. Shit I had to use litres upon litres of "S" smashing to get unstuck. Other than that I just breezed through MEI with an infiltrator using mostly the pistol, which came as a surprise to me since I recall using the Sniper Rifle a lot when I first played the game. As far as world building goes it's pretty good, very cliché but it's part of its charm and the scenery is very well designed in that it provides the illusion of being on a large world when you are actually confined in very small areas, but you at least get broad sights. For example, and I am getting into MEII, the Citadel in ME2 is barely larger than the Normandy and it feels so out of place... ME2 has much better cut-scenes, the red/blue interactions are arcadish but works well enough, though the reputation system which was already tied to persuasion in MEI makes a terrible step backwards in that it railroad you to either be a blue paladin or a red douche bag. I just couldn't stomach it so I just used a save game editor to give me more reputation blue and red rep points, problem solved! I can now freely chose my responses... well as freely as the dialogue wheel allows.
A brief comment regarding the dialogue wheel, yeah I get it, it sucks not knowing exactly what your Sheppard is going to say when you chose an option, many times I have regretted my choices but I am going to play the devils advocate here, would you play for hours a voiced content if you have to read a good part of the dialogue lines to later listen to them? My point is: the dialogue wheel is a result of the cinematic scope of this game's narrative, and it's actually the lesser evil compared to any alternative I can think of that doesn't involve removing the protagonist voice from it.
In regards to the story, I think ME2 is the bottom of the three games. It's a bare bones story that only serves as a background for all those retarded guys and gals you recruit who all have their personal problems and for some reason you are playing more Sheppard the psychiatrist than Sheppard the war hero. It's all just a little bit too much for me, can we get on with the Collectors already, pretty please! Well I guess it will be soon enough. Since I already played the game back when this shit was released I already know there's the suicide mission waiting for me. So I don't think this new edition holds any surprise for me, but it's still one of the best game endings in terms of tying it all up in a reasonable satisfactory manner, end boss excluded, that's just cringe.
After that I will play ME3, while I haven't had a feel of it in the Legendary Edition I expect it won't have changed much, this time I intend to install a few mods, unofficial patch and an expanded "take back earth" mod that supposedly makes the last mission more responsive to Sheppard's actions. I do remember being sorely disappointed at the ending, but with time I've come to expect it so in a sense I also came to terms with it being what it is and at least the rest of the game is mostly about Sheppard's war story, which is imo an improvement over ME2. Well anyway I will report on my feeling about the rest of the remastered trilogy when I finish it.
Btw: unless you are authistic and have way too much free time I recommend using two mods in ME2 that you can get from NEXUS mods, one that allows you to survey planets with one probe and one that skips the hacking mini games, they will save you so much time...