TL;DR: Get Civ V. Get it now.

This was the first game I ever played on Steam, and I couldn't ask for a better introduction to proper PC gameplay. Civ V (particularly Complete Edition) provides literally endless hours of enjoyment for all those who play it, with its iconic procedural map generation, rousing music and international diplomacy. No Steam library is complete without this game, in my opinion the best in the series and unlikely to be surpassed, barring a staggering development in Civ AI.

Of course, no game is flawless, and it would be inaccurate to leave a review that excludes shortcomings I know to be present.
The behavior of NPC civs is historically ludicrous, but that arguably adds intrigue and entertainment to what could be a dry game.
Automated exploration, a virtual necessity on large maps with large navies, often gets units stuck in loops around the same tiles (a minor inconvenience).
On non-Standard game speeds, long-term diplomatic deals often show "negative turns remaining", which makes diplomacy confusing in circumstances regarding when penalties will be dealt for declaring war.
Regarding war declaration: a passive, inoffensive human player can come under diplomatic hatred when an enemy attacks them; essentially, single player puts no emphasis on aggressor status in war declaration, laying diplomatic penalties on the player regardless.
Scenarios aren't available in multiplayer, which although not critical, is still disappointing.
Other problems exist, but don't come to mind at the moment.

Don't let those troubles stop you from enjoying the game, though; most problems are minor inconveniences that you learn to accept and adapt to as you grow as a player.