Alright, so enough about that. Greetings! I have been playing HotS since the beta, though I've mainly started playing the game MAINLY for fun (though let's be honest: Winning is much more fun than losing) after several salt-induced ragequits from the game for fairly significant amounts of time.
I'm someone that likes to play fluidly and tries not to follow guides too closely (ironic that I'm making one, right?)

Why the Cyborg Ninja Screaming Guy?
Genji is by far my favorite hero to play in the game since he has tons of mobility, decent damage, finisher that can have a cooldown reset, as well as a defensive that has a large potential for high-risk high-reward.
I would say that Genji's largest weaknesses are hard CC (though, according to Blizzard's 'Hero Spotlights', literally every hero's weakness is hard CC... go figure) and limited durability.
The reason hard CC really messes over Genji is that it interrupts his Deflect ability, leaving him incredibly vulnerable.

"What the hell do you know? / Why should I trust this guide?"
Honestly, I don't know much about anything in Heroes of the Storm, other than having memorized pretty a large amount of the heroes' abilities...
I only have 162 games as Genji with a 40.5% Win Rate (whoops), though I still love playing him. Mainly because I think that understanding his talents is a lot more important than trying to find the one mega path that "is the meta", which I believe really limits Genji's ability to be flexible.

Anyways, enough of my ranting and on to the actual content.

Shuriken: Throw three stars spread out in a direction, the poke ability.
Deflect: Primary Defensive and "lol, I can't believe Kael'Thas tried to Pyroblast me" ability.
Swift Strike: Major mobility and finisher ability.
Cyber Agility: Important mobility trait/ability.

Dragonblade: Swing your sword in an arc and hit people.
X-Strike: X-shaped ability with 2 damage parts.

Yes! I enjoy taking Dragon Claw at level 4! Here's why: (A) Doesn't require to hit people at the end of Swift Strike unlike Strike At The Heart(SATH). (B) Deals more damage than SATH and is not a DoT. (C) I tend to use Deflect on a regular basis anyways. (D) Total control on when to use it (once charged, of course) and gives Genji a great wave-clearing tool. and (E) It is an AoE ability so it makes it easier to hit multiple targets at the same time.
In my opinion, the only real downsides are that it has to be charged in order to use it and the visual effect tends to make it's effective area look smaller than it actually is.
Cool thing about Dragon Claw: Can be easily charged when your team is taking a boss or when there is a boss-like objective for the map (such as Mines or Garden), simply use Deflect right before the boss uses the AoE stun ability; Bam, instantly charged and take no damage (though, yes, you do get stunned).

In my experience in playing Genji opponents as well as looking at the information gathered by HotsLogs (which is not 100% accurate, though it gives a fairly good estimate), there are some talents which are completely ignored.

Note: This section is VASTLY opinion based, which has been influenced by my experiences while playing as Genji.

Level 1: Mostly mobility enhancements
Swift as the Wind: Great for when you think you'll need to pursue targets that you think might put distance between the two of you using blinks or other speed enhancements (Thrall, Tracer, Lunara, etc).
Agile Dismount: Haven't used this one a whole lot, but it is definitely useful when you want to increase your safety when a team-fight begins and then jump into the fray from a farther distance.
Pathfinder: The under valued talent, I take this one when there are enemy heroes who have gap closers, it essentially has the opposite use of Swift as the Wind: Escape. Jump over a wall, tower, or keep and you'll get the speed boost to outrun several heroes due to the 25% speed boost that lasts twice as long as Swift as the Wind (6 seconds).

Level 4: Offensive Enhancements
Shuriken Mastery: Very important if the enemy team has a lot of hard CC and may be wise to keep your distance from them, can also be a great burst tool when combined with other talents down the line.
Strike At The Heart: I am not a fan of this ability as it requires Genji to be fairly far away from his opponents and it is a DoT (which means that a Tracer could potentially survive this as well as invulnerabilities/stasis used by heroes such as Uther, Auriel, Chromie, Jaina, etc). However it can be incredibly useful if the enemy team has CCs and large amounts of mobility, the CCs will prevent you from being able to build up Dragon Claw.
Dragon Claw: (Basically everything I stated in "The Elephant" section)

Level 7: Mostly defensive abilities
Augmented Guard: Haven't used this one a whole lot, though I've had success with it against teams that are running several burst mages (both KTs, Jaina, etc) and if you can block a lot of their burst, you get a decent sized shield for 4 seconds.
Perfect Defense: My personal favorite, mainly due to its synergies with Dragon Claw as well as the level 16 Reflect talent.
Cyber Shield: Very strong against mages, works well with Shuriken Mastery, Double Jump, as well as Agile Dismount.
Dodge: Fairly niche talent that has main usage against heroes that hit slow and hard, such as the Butcher. Extremely useless against heroes that hit often and weak, such as Tracer, Twinblade Varian, and Valeera.

Level 10: The Heroics
Dragonblade: I personally have not used this one much. To me it seems like it requires the enemy team to not have a lot of CC, squishy targets, or silences. The few times I've had significant success with it is when there are several mages on the enemy team.
X-Strike: My personal favorite, deals decent damage though for me the most important part is the mobility, which allows Genji to pop into the enemy team and go into Dragon Claw or to simply create more ground between himself and the enemy team.

Level 13: Damage and Utility
Shingan: Great when you know you'll be in people's faces or when there are significant objectives on the map such as bosses. Best used when against larger opponents such as ETC or Cho'gall, though I tend to take it regardless.
Flow Like Water: Can get a lot of value out of it when enemies are clumped together nicely, great for when you like to engage with Swift Strike (though personally, I don't).
Double Jump: Goes well with Shuriken Mastery as well as Cyber Shield, allows you to recharge a large amount of Shurikens if you've completed the required quest for it.

Level 16: More damage!
Reflect: A very offensively minded ability, great for use against large burst abilities or just attacks that hit often, such as Li-Ming's Disintegrate or Tracer's auto-attacks. Has excellent Synergy with the level 20 Zanshin.
Final Cut: I am not a large fan of this ability, as enemies can generally avoid it if they are paying attention.
Steady Blade: Similar to Flow Like Water, great when the enemy team likes to clump together a lot.

Level 20: Heroic Upgrades and Powerful Effects
The Dragon Becomes Me: Fairly self explanatory, get lots of value when you can hit a large amount of targets.
Living Weapon: Similar to The Dragon Becomes Me, great when you can hit a lot of enemies at the same time.
Sharpened Stars: Essential talent if you're going for a Shuriken build, as it allows Genji to hit enemy heroes that are hiding behind other units, be it minions, other heroes, objectives, structures, and so on.
Zanshin: A really fun talent if the enemy team is not coordinated well, can melt the entire team if you can block a Li-Ming's Disintegrate or a large burst ability such as Kael'Thas' Pyroblast. A very large amount of the time that I choose this talent, I generally already have the quest completed.
Important Note about Zanshin: The quest builds up even before you get the talent, you can check your progress by hovering your cursor over the Deflect ability.

If you've made it this far I simply want to say thank you for taking the time to read my guide.

I will say it again: Playing well in HotS does not mean following what the top of the top-tier players do. I play to work well against the enemy team, knowing that I myself am no where near Master rank.

Hopefully this guide will be able to provide some use and feel free to leave a comment.