What is the order of the Doom Original Series?

The official classic canon would be:

DOOM

DOOM - Thy Flesh Consumed

DOOM II

DOOM II - No Rest for the Living

Sigil is unofficial, as are The Master Levels for DOOM II and Plutonia. TNT: Evilution IS considered low-canon, but I'm really not sure where it fits in though. Given the lack of events to gauge context, we'd have to go on the visuals and equipment - this puts it somewhere DURING both DOOM and DOOM II, which seems odd. Between, perhaps?

As mentioned, DOOM 3 is something of a soft-reboot, so you can consider it a recap of the above canon. Play through the above DOOM and DOOM II canon, then play through DOOM 3; it's a more horror-esque and narrative-heavy "remake" of the previous two titles, and overall a really solid game.

Another note; The Ultimate DOOM is a comprehensive collection of DOOM (1) canon