Flagship (the one Weapon)
The Flagship makes for one of the best build-arounds if you're going for a one-weapon Vanessa. Its main challenge is finding a Tool, Ammo, Property, and Friend to hit its 5x Multicast threshold.
By building around this, you can create a massive burst engine that will dominate most early matchups and put you on track for a Day 10 win.
You can find it somewhat easily by looking for the Pol vendor, which sells Large items. While you're there, you can also look for your next core item, the Crow's Nest.
Crow's Nest (Property Activator)
The Crow's Nest qualifies as your Property activator while giving your Flagship a huge boost in Crit, along with Lifesteal, which is your main source of survivability.
Tool Activators
Some of Vanessa's Tool activations can come from sources like Honing Steel, Lighter, or Powder Flask (ideally you want something small, but you can also look for potent choices from other heroes like Battery or Multitool.
Ammo Activators
Since you're going to want to keep Flagship as your only Weapon, you can look for Potions or Nesting Doll as your source of an Ammo activator.
The aforementioned Battery counts as both a Tool + Ammo so it's a great chase item for board space economy.
Friend Activators
Vanessa usually has a lot of Aquatic Friends to choose from, but if you hit the Oceanic Rush Skill, you'll want to adjust your gameplan a bit to make sure it hits your Flagship.
Oceanic Rush
Pesky Pete, which can drop from the Bloodreef Captain PvE encounter, makes an ideal choice for Vanessa but any non-Aquatic Friend can work, such as Bomb Squad or First Aiden.
Pete fits particularly well however since he can be positioned next to the Crow's Nest for its adjacent activation.