1995 Trans Sport Engine Dying While Driving

We just purchased a 1995 Pontiac Trans Sport with a 3800. The vehicle starts good. However, as we are driving down the road, it seems like no fuel is getting to the engine for a few minutes and either dies or fine after a minute or so. Our mechanic is baffled as to what is causing it. It does this more so when low on fuel. When we have the problem, the RPMs go down to about 1000. When and if it dies, we pull over and kill the engine and let it sit for about 3 minutes, then it starts up fine.

We are not mechanically inclined as to what to do about this.

Any suggestions would be appreicated.

... if it dies, we pull over and kill the engine and let it sit for about 3 minutes, then it starts up fine. .
...THen what happens next?...Once it has restarted, will it repeat the same trick or is it OK from there? If fuel starvation is the problem, it will probably just get worse .
Will it stop if you just let it idle on the driveway ?
IF we center on fuel starvation, the fuel pump will be a likely candidate, but if you can duplicate the problem sitting in idle, I'd go for a fuel pressure test before dropping the tank.
www.avigex.ca/xport/fuelpressuregauge.jpg Pressure should be around 40 psi.
www.avigex.ca/xport/fuelpressuretest.jpg
DO you clearly hear the fuel pump buzz for 2 second when you first turn the ignition to "ON" ?
DId your mechanic change something?...like the fuel filter (inexpensive and rarely the culprit, but at least it clears this option...)

When sitting, it will sometimes continue to idle roughly, then pick up RPM again. Sometimes it will die. In either situation, we will then drive it (anywhere from 5-15 miles) and it will repeat again.

Yes, we hear the fuel pump when the key is turned. It lasts for a few seconds.

No, the mechanic changed nothing as far as the fuel goes. When we got the Van, we had all of the brakes, brake lines, etc. changed. The TCS light was on and there were so electrical problems. However, once the brakes were changed the TCS light eventually went out after a few days. The electrical problems were solved with him checking the fuses. He thought the dying problem was due possibly to the TCS light and/or electrical problems. Never considered fuel problems. We got it back from the garage on Friday and drove it yesterday. Upon driving it then, we realized it was fuel and not either of the above.

OK...before dropping the tank and committing for a fuel pump, best would be to have a fuel rail pressure test, specially if you can make it to happen sitting in the driveway.
The pressure tester shown above was done using an a/c recharge kit by removing the bottle adapter and ball check valve from the other end, and a standard pressure indicator. I do not know why, but "readily made" fuel rail pressure tester are hard to find...and probably unduly expensive..
Of course the fuel filter is a simple and inexpensive maintenance item...even if it does not solve the problem.

I'd start by changing the fuel filter. As LMP said, inexpensive and should be done.