Interesting question. Not easily answered. Ok. My opinion.... Standard screen size for a tile-based game.... Because everyone has the potential of having different screen dimensions, going with what "fits all", is the place to start. Tile size has a say in it as well. If you are using 8x8 or 16x16 or 32x32 etc, make sure that your map can fit evenly for the screen you chose. eg: 640x480 @ 32x32 will give you 20x15 tiles. 1024x768 @ 32x32 will give you 32x24 etc.. Starting with either of these sizes would be fine.
Old classic tile-based games were "fixed screen". ie: Get across the screen to exit; new screen is drawn; player back to left of screen. Then along comes screen scrolling. Suddenly the "camera" can now "follow" the player across, what seems to be, an "endless loop" of scenery. ie: Mario Brothers. My suggestion. Start with a "fixed" screen. "Scrolling" will give you a "nicer feel" to the game but as I have almost no experience with scrolling, fixed is all I can suggest.....
I not sure if all this helps. If not, I 'am' sure, that the other guys would have better suggestions... lol
J