Civilization V: Complete Edition is very accesible and often on sale for next to nothing. Multiple difficulty settings and tons of replay value (100 hours+) if you so wish.

But beware: Alpha Centauri has a high difficulty!

Not much to add here I can recommend Disciples 2.

4x
Galactic Civ series (preferably 2)
Stellaris
MoO series (1+2)
Civilization series

RTS
Age of Empires
Command and Conquer
Red Alert
StarCraft
Company of Heroes
Close Combat

TBS
XCOM (any old or new)
Ageod titles (stick with small scale games for starters)
Unity of Command
Europe at War
Strategic Command
Combat Mission

Global (paint the map style)
Hearts of Iron series
Europa Universalis series
Total War series (stick with early titles for better AI and battles)

Any of those games (with the exception of Ageod) are really good beginner-novice strategy games, and aren't too difficult.

WH40k Dawn of War did that to me. Wasn't into strategies, then proceed to buy every expansion pack for DoW.

If you don't have trouble with it, a lot of Space Empires IV can be automated to ministers who will take care of tasks for you. (Note: Never turn on the political minister unless you want to unknowingly declare war.)

Populus 1/2 are overall simple in the management aspect, but can get quite hectic.

Knights & Merchants is more about logistics than combat, that was an RTS I played the heck out of back from the Demo CD era.

Warzone2100 is free and open source, as is OpenTTD; can't go wrong with trying a free game.