If your native res is 1280x800 or lower, native. But most of us use a resolution higher than that, and this game is pixel-based, so being able to use a high native res is functionally useful.
To enable higher resolutions, make sure you have the version 1.02 patch installed. Then, apply the downloadable patch. This patch changes the maximum size of the CivNet window from 1300x1048 to 32000x32000. It is designed for version 1.02 of civnet.exe, size 2,073,600 bytes.
Bugs & Limitations
Although the overall CivNet window will stretch to 32000x32000, the maximum size for the map window is calculated dynamically, depending on the zoom level. At the default zoom level, the maximum map width is 2570 pixels. This is just wide enough to show the world all the way around from west to east. In other words, there wouldn't be any real point in stretching the window further, since there is nothing else to display. (If you really want to fill a 4000x3000 monitor, you could try increasing the zoom level: this should let you make a larger map.)
This leads to a minor bug though: if you stretch the map all the way to 2570 pixels, the currently active military unit (the blinking one) disappears. If you watch the minimap as you resize the main map, you can see a yellow rectangle, telling you how much of the world your main map is showing. When this rectangle disappears, you have gone too far; just take it back a few pixels until the yellow rectangle reappears in the minimap and your active unit reappears.
Technical Details
The patch changes the hex bytes at position 0x147cff from 18 04 68 14 05 to 00 7d 68 00 7d.
The two bytes at 0x147d02 (1,342,722 in decimal) control the maximum width of the window. Likewise, the bytes at 0x147cff control the maximum height.
I've tested the width to 32000 by resizing the window offscreen, but I only tested the height to about 5800 pixels.
