Should be no problem by keyframing the parameters, so it's not clear to me where you are having problems. The simplest way to get an exact number would be to use a Layer Grid emitter - set it to the desired x and y density in the Options, then set the number of particles to match that value (which apparently only can be x multiplied with y), then animate the Particles/sec. property to only give one burst, e.g. by setting the number to a few 100 first and after only 5 frames animating it to zero. During those five frames all particles should have had a chnace to be born. For the actual path simply use the Motion Path option in the Air physics model based on a light. Either that or you will have to balance out the Inherit Velocity from Motion option with Air Resistance so the particles seem to swarm around the emitter. Likewise, you could use a Radial Field to capture and constrain them...
Thanks for the advice, Mylenium.
Before you replied I think I was able to figure the problem out. What I did was 1) Create a keyframe for particles per second. I set it to 75. I then jumped ahead one frame and changed the particles per second to 0. That seemed to do the trick. I then started my animation from that second keyframe and all was well.
I still having issues trying to bend Particular to my will, but each day I learn a little more.
Thanks again for your help.
I just found out that I don't have Particular installed right now, so I can't check the actual terms.
But in the options dialog there's something like a "pre-run" of particles, ie a number of particles that exist before frame 0.
So, you should be able to have just those particles and not spit any more.