I have a pretty huge backlog of games I want to / Have to play. I will provide the games to chose from, and a small comment on it that might be of help.

Uncharted 2 (PS4) - First game was ok, didnt really sell me the franchise though.

Batman: Arkham City - Armoured Edition (Wii U) - Never played a game in the franchise

The Legend of Zelda: Twilight Princess HD (Wii U) - Havn't played the original, Windwaker is my fav 3D Zelda.

Tomb Raider: Definitive Edition (PS4) - Havnt played TOmb Raider since the 90's

Fallout 4 (PS4) - New to the franchise

Doom (PS4) - Love me some Doom, but never really enjoyed FPS games on console before.

I want to play them all, just cant make up my mind. Pick a game and say why I should play it.

Uncharted 2, is the best Uncharted game.

All great choices. Just know that the difference in quality between Uncharted 1 and Uncharted 2 is night and day. Uncharted 2 is so much better.
Also,
- I think Wind Waker is more fun. But TP is more... western.
- I think is better to start with Arkham Asylum :D. Is very Metroid like. Arkham City is more like Assassins Creed.
- Tomb Raider is a bit Metroid like. Definitively has more emphasis on exploration than Uncharted, which is more of a linear action game.

Uncharted 2.

It's probably the shortest game next to TR and the better of the two since TR has really shit story telling and characters. It's like a Bollywood production.

Batman is awesome. Arkham City is still my favourite Batman game.

FO4 & Zelda are probably the games that need the most dedication so you it might be best to start them after completing the shorter games.

The 2 best games of the list are: Batman Arkham City (best Batman game since batman NES) and Tomb Raider (Best Tomb raider game since the first one)

Uncharted 2, while fun, feels dated compared to those 2

That's good lineup.

Twilight Princess

You should play it now so you have well enough time to recover for Breath of the Wild.

Hopefully I will see a clearcut winner within 48 hours. So far.. it's not really helping hah ;)

Tomb Raider would be the best choice in my opinion.Personally I think its superior to Uncharted, and since Twillight is different than Wind Waker( even though its still an excellent game), Tomb raider is probably the better choice.Plus it lats around 15-20 hours, so you can clear it relatively fast.If I had to name a second, I would go with Batman.

When you only list excellent games thats bound to happen lol