So most printers print at 300dpi. Some can print higher, for example, this 100k DPI printer.
You want to work at a resolution that's higher than whatever you plan on printing for. And the more specific your details are, or the smoother you want your lines, the higher you want to be.
I do 350dpi because I work with detailed brushes/lots of color/lots of blending/lots of FX, and doing that sort of stuff at 600dpi would just make my computer die. If I was doing just lineart type stuff, or if I had a beefier computer, I would work at 600dpi.
One thing you could do in a lineart + color + FX sort of style (basically a typical comic style), is to do your lineart at 600dpi, then compress your image down to 350 dpi for your colors and FX. So now you can have the best of both worlds.
Something to note about canvas size, US paper comes in different sizes from the paper that the rest of the world uses (because we just like being special).
The paper that most countries use is based on the golden ratio, and so if you use A5 you can scale up to A6 or down to A4 with no trouble (except for pixelation when scaling up of course.)
US paper works a bit differently, basically, each size is proportional to half the size of the paper above/below it. (except for legal-sized paper. For whatever reason that's different)
For my minicomic, I knew that I was going to print on 11x17 (tabloid) size paper, so each page of dust is on an 8.5x11 (letter) sized canvas. This made the main PDF that I used really easy to make, HOWEVER, I also made a standard-sized-zine PDF that could be printed on 8.5x11 sized paper. The thing is, 8.5x5.5 sized pages ARE NOT proportional to 8.5x11, they're proportional to 11x17 sized paper. So I had to do a lot of tweaking to make my standard-sized zine.
EDIT: In the future, when I make other zines, I probably will not have the opportunity to print on 11x17 sized paper, so I'll plan to print on 8.5x11 instead. In which case, I would make my drawing canvas 11x17, because that is proportional to half of 8.5x11 sized paper. It's dumb and confusing, I know.
Yet another reason to move to Canada I guess?
EDIT: Legal sized paper makes really nice 1page/fold zines, just FYI.
EDIT2: To be clear my computer (a 4gb Surface 3) CAN handle doing painterly type stuff at 600dpi, but it's slow. Chances are, most computers out there can handle working at 600dpi if you HAVE to, it will just be kinda slow. I think it's very unlikely that you would HAVE to upgrade your computer in order to handle larger file sizes like @sandpaperdaisy suggested unless your computer is very old or has about 2gb of Ram. Also, some drawing software is more resource intensive than others. I have trouble at 350dpi in photoshop, but In CSP it's fine. If I had SAI (very lightweight program) I could probably work in 600DPI with no trouble.