I'd like to clarify the resolution question real quick.

The appropriate size depends on the end use of your map. DPI is solely a printing issue; if you're never going to print, you can safely ignore it. If you are going to print eventually, you need to know what size and the approximate viewing distance. 300 dpi is a bit of overkill for most poster sized prints because it's relatively unlikely that anybody's going to be looking at it closely enough for that density of ink to matter. As a general rule of thumb, if somebody's going to be looking at the print at less than arm's distance, I use 300 dpi. For 24" x 36" or bigger, I don't usually go over 180. A battlemat would be about 200. Multiply the size of your print in inches by the dpi, and you'll get the size you need in pixels: 24 x 36 at 150 = 3600 x 5400 pixels. 8 x 10 at 300 = 2400 x 3000 pixels.

If the map is only going to be viewed on the screen, dpi doesn't matter*; only the actual pixel dimensions do. If you want the entire map viewable on a 1024 x 768 screen, it needs to be around 1000 x 720 pixels (leaving room for "chrome"—file bars, scroll bars, and the like). That's pretty small for a map, though. Everybody has a preferred way of working. I don't like to go down below 4000 pixels wide, myself. And I don't often design for print; if I did, I'd probably start even higher, as suggested by the numbers above.

* Some people like to reappropriate dpi to help make battlemaps for virtual table tops (VTTs) such as MapTool. For standard D&D maps, 1" = 5 feet. If you substitute your dpi for the 1", you'll get a number of pixels = 5 feet. That is, 200 dpi means each square on the grid is 200 pixels wide. That's pretty well the maximum people like to use in a VTT. A lot of users go clear down to 50 pixels per square to improve transfer time.