Your PC should be fast enough.
Modeline refresh speeds are determined by maths - more vertical lines means slower refresh speed, regardless of how you do it.
Therefore, 288 line modes have refresh speeds closer to 50hz, not 60hz.
Modes like 352x288 will be slower that 288x224 (close to the mode your game Contra would have originally run in, monitor turned vertically) as they have more lines to draw.
So, playing a game like contra is going to cause problems when run on a horz monitor in 352x288 because of screen rate mis-match. However, you can minimise these problems with approriate settings in your .ini files.