Here you can find the dps in comparison of most of the builds you can get out of the adattability items i put in the guide, along with the standard crit builds. NOTICE all dps shown is just autoattacks, so crit is defenetly starting ahead.

Kraken slayer build: 1650 DPS
Shieldbow build: 1500 DPS

Ravenous Hydra + Black Cleaver: 1350 DPS (provides healing and armor reduction along with great waveclear and survivability)
Death's Dance + Black Cleaver: 1320 DPS (great if your enemy teams has a lot of AD damage and some tanks)
Titanic Hydra + Sterak's Gage: 1400 DPS (provides a great healing and shield from sterack thanks to the bonus HP)
Titanic Hydra + Black Cleaver: 1440 DPS (consider the armor reduction does not show up cause the dummies i tried the build on for the DPS check had no armor)
Edge of Night + Sterak's Gage: 1250 DPS (consider you have lethality and bonus dmg on abilities, this does not show up cause the dummies i tried the build on for the DPS check had no armor and i only used AAs)

From the results shows up that crit build scales better late as expected, but it gives less survivability to burst and getting caught, it's early game is way tougher as it gets bullied by most adcs and supports and most importantly Q deals way less damage in the crit build, and does not proc the buffed auto attack of spellblade.
The build i created and recommended i can't tell if is stronger than the crit counterpart, but it is a different way of playing the same characer, that may work in your games and provides a lot of fun, adapt to what you find in your games, that is the fastest way to improve.

If you want to dominate lane (often difficult at a low level, only if playing with thresh and a few other early game dominating supports) or if the enemy has a very oppressive engage, take Doran's blade.
If what you need is sustain against a poke lane take Doran's shield.
In any other situation go for cull, it's always a good purchease as it allowes you to scale if you are not very confident in your kalista skills.

On your first back you always want to buy the tear, this will allow you to spam Q and E to farm more freely and bully your enemies, along with that you can take sustain by buying vampiric scepter or go for tier 2 boots, that will allow you to be a hard target for hard engage champions, as your passive jump goes further with better boots.

Let's get to the core: rushig BORK will get you the chance of taking some early kills and being a very annoying laner, also thanks to your Berserker's Greaves, you will be able to take short trades, escape dangerous situations and lifesteal for some sustain.
Second item you are going to finish your Manamune, this will fasten the stacking of your tear and get you some good amount of ability haste, not to mention the on hit damage and bonus AD when it transforms into Muramana; consider finishing your Manamune before BORK if your lane is going particularly good, this will lead you to getting Muramana's powerspike earlier and end the game much quicker.
Always consider getting healing reduction or defenses as soon as possible when stuff gets scary: decide in advance what adaptive items of the next paragraph you are going to be building and counter your enemy laner: don't forget Kalista loves scaling and this build is not an exception, save some gold to defend yourself and it will always be worth it.
But let's get to the juicy stuff: doing some math you will see, getting your Trinity as your third item will grant you 180% bonus attack speed (Legend: Alacrity rune with 125 minions and no champion kills at level 11), and considering kalista's base attack speed is 0,694 this brings you to 1,94 attacks per second midgame, along with add the onhit from Muramana and BORK (up to 60 damage every attack for BORK and 62 every four seconds for Muramana), the 12% lifesteal, the 25 ability haste (20% CDR) the bonus AD (gets to about 260 total AD, 142 from items and 107 flat), plus the trinity effect spellblade, that makes your auto attack right after a spell to deal about 550 damage (1.5 second cooldown; it's very useful to lasthit muliple champions in teamfight, in fact after you have killed someone with E you can burst someone else down and repeat on your next target)... let's say those are pretty high stats for midgame.
Applying this infos to the ideal short trade this means throwing your Q and jumpin towards your target to follow up with a singe autoattack (and jumping backwards to safety) deals about 1100 damage, if you then use your E those will be about 300 more damage, this is examples on targets without any armor of course, but that's still a high amount of damage.
Consider you are pretty tough to kill thanks to your runes, that grant tenacity, a shield, boneplating and a high amount of lifesteal and damage coming from conqueror. Assassins won't be having the time of their lives.

Let's run through these items to see when and why you shoul build them, but take notice at two things:
1) don't build additional attack speed as you will get to 2.4 anyway thanks to Trinity's mythic passive;
2) it's not a great idea to build crit items since not getting a high crit chance doesn't give you the scaling that crit builds are good for.
For both of those reasons you won't find Runaan's Hurricane in this list, which was a core item for most kalista builds but just won't fit in here.

Black Cleaver: it is great against tanky matchups, it shreds the enemies' armor and deal on hit bonus damage to champions hit 6 times; along with BORK they do a great job at melting tanks

Ravenous Hydra: great for sustained combat and splitpush, 15% omnivamp is a great statline

Titanic Hydra: if built along with a Black Cleaver or Sterak's Gage it provides better damage and 500 more HP than his counterpart, but loses the 15% omnivamp. if the enemy team is full of assassins go for this one along with sterak's.

Death's Dance: great item against AD burst damage; if enemy team has a zed or kha'zix you defenetly want to have this one

Chempunk Chainsword: great against health regen mosters such as Mundo and Vladimir, but enchanter suports too such as Yuumi and Soraka

Mercurial Shimitar: only build this item if you are desperate for it's active, for it gives crit chance and as said earlier you don't really need this stat; overall there are better anti-mage items

Maw of Malmortius: this one is a great anti magic burst item, but i suggest you see what's coming up next before buying this one

Edge of Night/Sterak's Gage combo: if you are scared of unexpected crowd controls but not about magic damage in particular this combination of items is really great; the edge of Night grants excellent stats for a kalista, in fact lethality is always good to shred low-resistance enemy champions and the AD is pretty high; if you buy this, anyway, it must be for it's passive; what kalista doesn't really crave for is HP, but that's where Sterak's shines: granting a good amount of healing in combat along with a shield that procs when you go low on health; both the healing and the shield scales on maximum health getting (up to 200 health regen over 6 seconds and a 770 HP shield at full build)