If you're looking for the 19" variety, you're almost positively stuck with a 15khz (standard res/ CGA) monitor. This is what 90% of all arcade games are, so all the mame games will look nearly perfect. A computer monitor is much easier to use, but it won't look as authentic and since it's so crisp, the games will likely look blocky. When you say new games, do you mean newer arcade games or console games? Many current arcade games are still 15khz. There are some 31khz (high res/ vga) games out there, but aren't likely emulated in mame, like Naomi. If you only plan on using Mame, then a regular 15khz monitor will look the best and keep the price under control. I can't recall any medium/high res monitors in the 19" range. The ultimate monitors are called tri-sync (15/24/31khz) and they start at 25/27" and many hundreds of dollars. You can look on ebay or the forums and usually find a used 19" monitor for a decent price. I've had mostly WG, but Electrohomes are also very popular and reliable. You need to first pick your price range and that'll determine what your options are.
Scott