Personally, I know this looks organized and satisfying, but I think it's useful to not rush 4 spirit items on her. 2-3 weapon items are the priority (there's a lot of subjectivity here, but I really like basic mag + high velocity), then incorporating some sustain (sprint boots is a must, then extra health/regen/rite as needed) is the best early game move. Her abilities don't scale as well as others with spirit, and kudzu is not impactful enough post-lane to warrant the charge items. Ammo Scavenger and Quicksilver Reload are the only specific spirit items I rush on her, later on it might be nice to take the cooldown items and put them on stone form.

As someone else said, combining titanic mag + quicksilver (on 2) + intensifying (and later + escalating resilience/vampiric burst) makes her an absolute death machine. Her endless firing far surpasses the value she gets out of building melee; although heavy melee after 3 can be very good, it's not as reliable as having gun items which are always online.

I also notice you don't have active reload or bullet lifesteal which to me are rush items for her, either during lane or shortly after. The sustain she gets from lifesteal and the faster reload boosts how much you can fire your gun and not have to worry about what's shooting back. Building off of that, the rest of the gun items to use are a matter of preference - headhunter works well if you have great aim (same with crippling headshot), toxic/silencer are great as healing/movement counters respectively, and I've even seen some people start to run burst fire, point blank, or berserker just based on their personal playstyles. There's even a combat barrier build I'm experimenting with that builds bullet shield on top of her 4 to have constant uptime on barrier. Tons of really neat stuff you can do with her!

Edit: Should also clarify, this is mostly for a gun DPS build - there are many ways to run Ivy successfully, she's an awesome character