OK, after a lot of thought, I'm going with Option #1.

PS2 is arguably the best console of the sixth gen. It had great games like Ico, Devil May Cry, Snake Eater, The Precursor Legacy, Going Commando, Up Your Arsenal, Grand Theft Auto, Shadow of the Colossus, and many more. Plus it supported ports of Half-Life and Deus Ex.

Wii is arguably the best console of the seventh gen, supporting masterpieces like Xenoblade Chronicles and Super Mario Galaxy 2. 

And XOne is pretty darn good too. It might be lacking in quality exclusives, but it supports most third-party content, including gems like Shadow of Mordor, Shovel Knight, Rocket League, and Mortal Kombat X. Plus I can play the original Gears of War and a bunch of old-school Rare games via Rare Replay.

In that case, I'll go for option 3. The PS3 is my favourite console of all time. For starters, it has the absolutely superb Ratchet & Clank Future trilogy, but it also has remastered collections of the original Sly Cooper, Ratchet & Clank and Jak and Daxter trilogies. Furthermore, it has Sly 4, another one of my all time favourite games. To me, those alone make it a must have, but if you include all the tons of other great games it has, including tons of multiplats, AND the best of the PS2 library (GoW collection, Kingdom Hearts 1.5 and 2.5, MGS collection etc.) it makes it my favourite console ever, by a fair margin as well. 

The Wii U has a pretty good library as well, and what's especially enticing is that it has remasters of both Windwaker and Twilight Princess. Throw in Zelda U, and it's an awesome console to have for someone like me who wants to get into Zelda (even without including BC!). I'm also a fan of platformers, and in that regard, the Wii U's library is loaded.

As for the Xbox... yes, I'll miss out on a lot. It wasn't really until the 7th gen that MS really got going in terms of the Xbox imo, but there are still some gems there, like Blinx, Halo 1&2, and a few more. While it would've been nice to get Gears, Lost Oddysey, and more that it got during the 7th gen, that option wasn't available to me

Does the PS3 have BC on PS2 games?

Edit: lol nvm forgot to read that last bit

So glad we're getting votes for all three!

I was worried one might dominate the rest. Phew!

For BC clarification, would you consider the fact that I can buy various PS1 and 2 games on the PS4 as BC?

This whole idea might be a bit more interesting if the digital repeats were removed from consideration as well.  Something like a scenario where all the indy titles got physical releases and you couldn't connect the console to the respective online storefront, what would you pick type of deal.

After a bit of thought and even without BC I still have to choose 

Option 1:
PlayStation 2, Nintendo Wii, Xbox One

PS2 -  It has everything a fan of JRPG's wants and some of my favourite games/series: Shadow Hearts, Xenosaga, entries in both the Wild Arms and Suikoden series, Rogue Galaxy, Okami, SMT Digital Devil Saga, Atelier Iris , Dark Cloud,  Disgaea and La Pucelle Tactics, FFX and Kingdom Hearts to name a few and I could keep going but I will leave it at that :) Other than that it also has a very large library of games and that would give something for everyone.

Wii - I was never really into the Wii and I was part of the motion control hater camp whilst it was about but recently through BC/VC started to appriciate it has a good solid library and Mario galaxy, Metroid Prime along with Twilight Princess and Skyward Sword as well as Xenoblade Chronicles ,Smash and Mario Kart are solid additions along with plenty more.

Xbox One - Rare Replay has so many classics that are on this console and has the Forza racing sim and the open Horizon series, Hosts some of the greatest shooters around especially when it comes to multiplayer with Halo 5 and the upcoming Gears 4 as well as been able to play the entire Halo series through MCC and the origional gears of War remastered, It also has Sunset Overdrive which is one of the games of the gen so far.

After typing this I kinda began wondering did I do this right are you after the opinions on the best combo as in if you had to choose only one route through the 3 generations or more of best combined overall library? I kinda did mine as a best overall library as I thought these 3 consoles would compliment each other and tick every box for what is needed in a game library but it would definitely fit as the best combo to go through the gens also.

I think that is the fun of this type of question.  I went with the option I picked mainly because of my lack of experience with a console like you did.  Thinking about it further, makes me wonder if leaving out the PS2 is such a good idea.

I think removing PS1 classics and Virtual Console makes the most sense. Otherwise, Wii pretty much supports NES through N64!

I agree.  I made my selection based solely on the available library that is exclusive to those consoles.  Even remasters are still exclusive in the sense that they are their own entity even if they tell the exact same story.  Though, in the same token, Wii supporting gen 1-5 doesn't infringe on the gen 6-8 criteria.  Though the PS4 allowing for PS2 game purchases does.

Option 2 All three consoles are awesome. Option 1 Only has one console that I like (PS2). And Option 3 has two good consoles (PS3 and Xbox) and one very mediocre console.