Most of the cores for MiST can work without the scan-doubler, so provide a 15KHz output via a VGA - SCART cable. Great if you're still using a CRT.
Depending on the LCD screen you use, you may find a TV with a SCART input (I use my MiST on a 37" LG LCD TV). If SCART isn't available, then as mentioned, many cores now support component output.
Finally, you have the option of enabling the scan doubler and using a direct VGA connection. Depending on your screen, it may not sync down to a 50Hz refresh. My TV won't (but then I'm just using SCART anyway so don't need VGA). I so have a smaller monitor that handles 50Hz if necessary. 60Hz through VGA is within standard anyway, so NTSC versions of cores should all be okay through VGA.
Atari equipment all in storage - Now playing with MiST