I use something called a Pentel Pocket-Brush Pen, which is like a cross between a fountain-pen (with replaceable ink cartridges), and a brush. It has an actual synthetic-bristle brush on it. When the cap is on firmly, I have never had it dry out between uses. The ink cartridge means you don't have to keep dipping a brush in ink to load it, you just keep going until the cartridge runs out. (I think it took my first cartridge a long time to run out, too, about 6 months, or at least 40 drawings.)
They're not hideously expensive, either -- I've seen them listed for between $12 and $20.
Prior to that, I used the flexible felt-tip Sakura Pigma Brush Pens. I liked those okay, but I found they didn't last all that long -- not that the ink ran out, but the tip of the felt "brush" thing would fray and become not-useful for fine lines. So I got tired of buying them so often. The Pentel one is definitely way more cost effective. I bought one like 2 or 3 years ago, and I still haven't run out of the packet of 4 cartridges it came with.
(I also find that the real brush on the Pentel is that much more versatile.)
Both are so cheap that you could probably afford to get both and experiment with them.
Er... about water-resistant ink. Um. Well, both of those types of pens are supposed to have water-resistant ink. But I have never really trusted that. So I use a method in which I do all my inking, scan the linework at a high resolution, do clean-up on it in Photoshop (and I ALWAYS have to do clean-up), and then laser-print it out on the type of paper I want to color on. Laser-printed lines are absolutely positively waterproof and a really nice solid black.
I realize this method isn't for everyone, though. For one thing, it resulted in my buying the cheapest, smallest laser-printer that HP makes, and that's still not an insignificant cost. It also constrains you to printing out something to color at the size a printer can print out. (I often do my coloring in several pieces and assemble a larger piece out of the separate colored pieces in Photoshop.) And it works great on the types of paper I have used so far (on which I use either colored pencil or Copic markers), but I have never challenged it with toothy watercolor paper or anything.