Valla is one of the most complete heroes in the game and is an Hyper Carry for a reason. A well played Valla can be one of the deadliest heroes in the game.
This build is what I consider Valla's standard build since she can do a ridiculous amount of damage from afar by using her Multishot ability.

- Level 1 -
By getting Fire at Will not only do you improve Valla's W damage but you can make Valla enter her Basic Attack range almost at maximum hatred, maximizing her damage output right at the beggining of the fight.

- Level 4 -
Arsenal is an obvious choice because it increases the damage of Multishot, makes it's area bigger which facilitates hitting a larger amount of heroes in the same W spell (also helps stacking on Fire at Will) and it even gives you mana back, making it a less mana intensive ability. Always try to hit the most heroes on your W in order to maximize damage output.

- Level 7 -
I mostly take Frost Shot since it helps my team by applying some CC to our enemies and makes your next Hungering Arrow deal 25% more damage.
If you already have CC on your team or if your enemies have to hit a lot of skill shots, you can also take Hot Pursuit for the extra speed.

- Level 10
Strafe is a great ability to do a good amount of area damage,and you can use it in between a burst of abilities. It is especially useful when you can't Basic Attack frequently. If you need some CC, or if you think you'll be having a lot of 1v1 fights, you can take Rain of Vengeance. You can use it to lock down a target and completly blast them off, since it also does a fair amount of damage.

- Level 13-
For almost all builds I tend to use the same logic. If they have a lot of burst damage I like to take Gloom, otherwise Siphoning Arrows can also be a valid pick for burst healing.

-Level 16-
When playing a W oriented build I like to take Punishment if I can stay alive for long in a fight and get multiple Multishots off. Seething Hatred is an alternative when you can't really stay that long into a fight, making your W output more burst like.

- Level 20 -
Death Siphon can really be a death sentence for the entire enemy team. As long as you are hitting multiple targets you can basicly have it forever. I think it is a must for this Multishot build.

If Valla is able to safely basic attack the enemy team she can shred down any tank in a matter of seconds. This build is really effective against very armored and tanky compositions and can be extremely deadly if Valla can hunt her enemies uppon their retreat.

- Level 1-
Of course the core of the build must start with Creed of the Hunter. In order for this to be very effective you must be very effective by always basic attacking something (prioritizing heroes of course).

- Level 4-
Death Dealer gives you even more mobility and damage options. Just be sure to save it if you think the fight is about to end so you can safely escape but it can also be used to critically damage your opponents so use it often in the beggining of fights while always maintaining proper and correct positioning.

- Level 7-
Since now you have more attack speed via Creed of the Hunter, getting Hot Pursuit will increase your sttuter steping effectiveness in avoiding skill shots. To put it in other words, you attack faster, so in order to maintain your damage per second you move less while stutter stepping. Choosing Hot Pursuit allows you to maintain damage per second and to move more.

- Level 10-
I think Rain of Vengeance is mandatory for this Basic Attack build since it allows you to do some extra damage and to lock an enemy down. Since you will be constantly auto attacking choosing Strafe here can make you lose your single-target focus that you might need.

- Level 13-
As said before, if they have burst damage I think Gloom is a safer option. Otherwise, Siphoning Arrows will give you some burst heal that you'll need.
You can go Tempered by Discipline with this build, yet you must be sure that you can keep basic attacking, that they do not have burst damage available and it can be better against more tanky heroes.

- Level 16-
Manticore is mandatory here. You can just simply shred down anything. A good tip that not all players seem to utilize with this talent is that you should save your Vault to crit damage the third basic attack (Auto, Auto, Vault, Auto).

- Level 20-
For this one I tend to choose depending if I can auto attack very safely or not. If I can't auto attack so safely just take Farflight Quiver making you able to out range any structure in the game and making you able to poke from the safest distance you can possibly imagine. Don't take it against divers.
Instead, if you can basic attack safely or you think it is more useful to lock them down while they are escaping, you can also take Strom of Vengeance making Valla a machine gun essentially. This means that in order to be more effective you have to stand still sometimes (less sttuter stepping like Tassadar or Tychus).
Either one of these are really good with this build.

Last but not least the Hungering Arrow build can be used when you need to completly burst down a target. This one is really effective against low mobility divers, lower health bruisers and mages (like Malthael or Jaina for example). Although I think it is not better than the other two it sure has its place in a game.

- Level 1-
Puncturing Arrow allows you to deal even more damage through an extra Hungering Arrow bounce, but also makes you empower the damage and refunding mana if you hit it. This talent is great for massive burst damage, just be sure to use it as often as possible in order to stack it consistently. As for obvious reasons, if the other team has a lot of mobility do not pick this build.

- Level 4-
Not only this talent provides you with essentialy 2 charges of Hungering Arrow as it completly removes the mana cost of Vault, making you always able to escape as long as you don't waste the cooldown. I think it's easy enough to say this but do not E before using your Q, the correct combo should be Q, E, Q, Auto or Q, E, Auto, Q (depending if they can interrupt your second Q like Kael'thas stun)

- Level 7-
I almost always take Frost Shot for the extra damage off the combo W, Q, E, Q, AA. If you want to have an insane amount of burn on an Immortal or on Bosses you can pick Monster Hunter.

- Level 10-
Since this is a combo oriented build, you will not have it up all the time, so in my option, the idea is to throw your massive combo and then use Strafe for extra damage and kill confirmation. Rain of Vengeance is also a good choice, if you think you need to lock down your target to ease your Q hitting.

- Level 13-
This talent has the same logic, if they have burst take Gloom, else just take the burst healing from Siphoning Arrows.

- Level 16-
If I am able to be basic attacking and keeping my hatred at maximum, Seething Hatred can be deadly. Otherwise I like to pick Manticore to help confirming kills on higher health targets.

- Level 20-
It's very easy to understand, Acrobat will give you so much burst potential you can just blow their entire team up. I tend to use this talent in two ways, either W, Q, E, Q, ... or do W, Q, E, Q on one target, wait for my W to be up again, and repeat the combo several times, once for every enemy. Whatever you think is better for a certain situation, apply it.