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Age of Empires 2, for a while I had almost no other good games (exceptions: AoE1, Cultures Gold Edition, Empire Earth, Robin Hood, Zoo Tycoon) so I played that A LOT.

First Paradox game would be Stellaris.
 
First game ever or defined by platform?

First on Console:
Super Mario Bros. (NES)

NES_01.gif

First on Handheld:
Tetris (Gameboy)

tetris-on-game-boy-2.jpg

First on PC:
Indiana Jones - Fate of Atlantis (DOS)

IndyFateofAtlantisSteam_06-pc-games.jpg

First Tabletop:
"Mensch ärgere dich nicht" (don't know if there is a translation for it in english or if it was ever shipped outside EU/Germany)

220px-Menschenaergern.svg.png

EDIT:

NOW I feel old! =(
 
Something on the Atari, don't remember precisely. Probably Pac Man, Monkey Academy, Centipede, or Jump Man. I was 3 or 4 years old so it's pretty hazy. We moved before I turned 6, and I was winning Super Mario Brothers runs on the NES and had memorized how to beat 1st quest Zelda by then, so pretty significant jump in those 2-3 years. Then again I was like doubling my age so not surprising I suppose.
 
First Console Game and first video game overall: Super Mario Brothers.
First PC Game outside of School: Civilization, at school it was Oregon Trail.
First Strategy Game: Ghenghis Khan II Clan of the Greywolf

That last game to me was underrated, my mind was blown as a child: the portraits of your ruler, the BGM (each area had a track that corresponded to the region) It was awesome. Closest thing that came afterwards was CK2.
 
First Strategy Game: Ghenghis Khan II Clan of the Greywolf

Haha this game was fantastic. I even did the Mongol + World Conquest maps on my YouTube channel. I always wanted a mode that let you start as anybody...I think doing most of the abuses the game allowed any position would be winnable, though some of the old ruler + no heir combos or low body points + skills would be RNG.
 
Age of Empires 2: The Age of Kings
One of the best games ever made.
If you disagree with the point above I would like to point out the fact that there is still enough of a player base active on it still that the most recent DLC for it was released 17 years after the base game was released.
 
My very first videogame was Wolfenstein 3D, which I played on my dad's old MS DOS computer (we were really slow in upgrading computers, my dad likes to keep using stuff until it literally falls apart).
After we finally got a decent modern computer, my first game was Lord of the Rings Battle for Middle-Earth II. As a massive LOTR fan, that game was the best thing that ever happened to kiddo me.

My first Paradox game was HoI 3.