What I would like to know is what is the difference between a 15khz and 30khz monitor?
The number represents the number of lines the monitor can draw in one second. A 15KHz monitor can draw approx 15700 lines in one second. It means that if you want 60 frames per second, you are limited to 15700/60=261 lines per frame. You can't use some lines since they are reserved for the beam to travel back to the top left corner. In practice you can use 240lines at 60Hz or 288 lines at 50Hz.
With a 31kHz monitor you can use approx 480lines at 60Hz and 576lines at 50Hz.
Note that (almost) all graphic cards can output a 15kHz signal. The main difference with the arcadeVGA is that it got some 15kHz display modes in BIOS. This means that programs (e.g. windows and MAME) can use these modes directly without any special drivers.
Will I need a video amp like the one from ultimarc?
Depends on the graphic card and the monitor. Most graphic cards output 1V which is ok for most monitors but some (mostly older) monitors requires 5V and then you need an amplifier.
What brand of monitor do people recomend that is 24 or 25 inch?
For arcade use only it doesn't matter since it is mostly other features that differs. Find one that fits, physicly and electronicly, in the cabinet.