Engine chugging or missing

Have to service these a lot it's the MAP sensor ( manifold absolute pressure sensor ) this should fixya.

Diagnose the codes you have, when the check light comes on

If this vehicle has a double overhead cam, labeled DOHC on the engine covers, it can have a "Cam Phaser" problem. The chugging is caused by the cam timing being mismatched.
A sound is often produced by the engine such that it mimics a Diesel engine and the sound disappears above 2000rpm.
There is a lot of reading material about this defect on the Internet. Many other potential problems would usually be triggering a "check engine" light. Even a bad EGR valve would eventually show up.
About all that is left would be a fuel pressure problem, sometimes caused by missed reading on a crankshaft sensor.
Let me know of the cure once you try these.

if turbo charged diesel , have the turbo inspected and check the hoses for tight at connections

The in tank filter may be collecting debris inside the tank

The fuel filter is probably full of metal too. (fuel starvation) replace it.

OBDII engine diagnostics started in 1996. Since then, no mechanic worth his salt would ever start a diagnosis without reading the trouble codes stored in the computer. That's ALWAYS the starting point. Get the codes read and post them. Guessing without the code is futile.

starts missing after it warms up and on take off after a stop

the gas cap and check engine light thing are related in terms of the EVAP system, or the evaporative emisions system. This is NOT where your surge, or "chug" is coming from. The surge could be coming from a Exhaust Gas Recurculation valve that is starting to bind or "hang up" a bit. DO you notice this happens more at lights, or when coming to a stop? if so it could be an idle air control vavle.

Check engine light?