Car starts easily, but hesitates

I have a 1996 that will start up OK and idle OK. But, it will hesitate when accelerated. After warm up, it is drivable but boggs down if gas pedal pushed too fast.
It was running well last week with good gas milage and performance.
Were do I start to diagnose this problem.
There are no codes on the dash.

Partial answer in Grand Marquis forum. As an afterthought, how long has it been since the fuel filter was changed? May want to hook fuel pressure gauge to car and see if the pressure drops on acceleration. If it does, either clogged filter or weak pump.

I changed the filters, plugs, wires last week. No effect.
I'll check the TPS as you suggested and do the fuel pressure test.
How/where do I hook the guage?

There is a schraeder valve on the fuel rail that the gauge screws on to. It looks like a tire valve. Pressures should be 30 to 36 running 40 to 46 key on engine off.

...Been out of town a few days workin'...
Bought guage and did the fuel pressure test. The pressure is low and bounces up and down. I changed the fuel filter again(easy to do). same reading.

If the pressure is low and bouncing, more than likely the pump is getting weak.