Here is an entire review of many water-proof and water-resistant inks.
https://www.jetpens.com/blog/the-bes...en-inks/pt/829
It's not an exhaustive list as I'm sure they only include inks they sell but it's a good list with many colors.
Keep in mind that they type of pen you use is going to dictate what inks you use.
If you are using a classic metal dip pen you want a thicker ink that will hold onto the nib and flow only as you write. These are usually pigmented inks. Dye bases inks will be too think and watery and you will just lay down all the ink from your nib in one ot two strokes. If you don't mind using that much ink and the repetitive dipping then dye inks are fine with a metal dip pen.
If you are using a glass dip pen you can use just about any ink you want that wont permanently stick to the glass. Pigment inks may need to be thinned but can be used.
If you are using a fountain pen stick with only water based dye inks, anything else will clog up the nib and feed system. You cannot thin out pigment inks to make them safe so do not try. Also if your using a vintage fountain pen you will want to do some research on the inks you use as some newer fancy boutique inks like Noodlers have additives that can damage the ink sacks and other materials in vintage pens but newer modern pens will be fine with almost all fountain pen friendly inks.
If you use a brush then you can pretty much use anything you want.
If you decide to go with a carbon ink just get a large bottle of Chinese ink. This is one instance where Chinese is actually better as they have been making this kind of ink longer than any other country has been writing.
If you decide to go with Noodlers then you can contact Nathan and see if you can guy a large bottle direct. He's been known to sell Noodlers Black and Heart of Darkness in liter and gallon jugs to artists.