The main goal of this build is to spam Love (gun) as much as possible and finish up close. Make sure to choose the correct cards as this website does not display it right.

The Finer Things LVL 5: Might be the most fun/best card for Caspian. It allows you to become extremely fast for doing nothing, and with the combination of nimble you can take short flanks to take out enemies out of position.

Deadly Flourish LVL 4: I mainly use dashes for quick engagements/finishing kills. Getting a faster dash significantly reduces the risk of dashing into the enemy backline.

Casual Competency LVL 3: Spamming around chokes can land a lot of Rogue's Tempos, which will make BOTH the gun and the rapier shoot fast. I feel that 3 stacks is good enough (you will charge more stacks if you engage in a fight), but you can swap around a bit.

The Rose's Thorns LVL 2: It heals you a bit. Good enough.

In The Thick Of It LVL 1: Gives you ammo during fights. Helpful in some situations.

The two items that I would consider crucial for this build would be nimble and kill to heal.

NIMBLE: Combined with The Finer Things, Caspian becomes super fast and can surprise people with how quickly he can reposition.

KILL TO HEAL: Caspian kill. Caspian heal. Caspian Leave.

Some other considerations would be:
LETHALITY: MORE SPEED.
HAVEN: I would go for haven if I am playing more aggressive.

MORALE BOOST: Caspian's ultimate is pretty good and is usually able to get at least one.

LIFE RIP: Life rip kind of sucks on Caspian, but it can be situational.

Despite Caspian being a flank character, I prefer to play much closer to my team as the stun can lead to insane follow ups by teammates, or even allow an easy solo kill. That being said, it is also important to dive any target out of position and punish them the combo down below.

After getting up close with the movement speed by Love, I go for

WAR - ROGUE'S TEMPO - WAR - WAR (TRIPLE SLASH)
This combo will instantly kill any squishy

NEVER ENGAGE IN AN EQUAL FIGHT IF YOU DO NOT HAVE ROGUE'S TEMPO OR DEADLY MOMENTUM. YOU WILL LOSE.

Wasting your stun is devastating and you will die most of the time if you miss it in a close range 1v1.