Started my Civilization career with Civ2. Liked it at the time and though I was quite an amateur at the game. It was about a year or two later that Civ3 came out. Through Civ3, I was able to learn to play Civ2 better but I liked Civ3 better aside from missing the Wonder videos. Civ3 was a big advance for the series and a lot of things introduced in it still carry over through the other entries.
Civ4 took Civ3 concepts and almost went overboard in trying to flesh them out. Unit promotions, worker improvements, and custom governments along with the sprawling tech tree can make the game pretty dense. I thought it would be rough for anyone learning Civilization for the first time through Civ3 for the first time with the size of its instruction manual and concepts but Civ4 seemed to be even more daunting. Despite my Civ3 experience, it took me awhile to really get a grip on a lot of the elements in the game. Some of them you can discard. Unit promotions, while an intriguing concept, generally revolved around selecting a couple of the same upgrades over and over. I played Civ4 for a bit though not as much as Civ3 which is my maximum exposure to the series.
Bought Civ5 when it came out and was intrigued by its new map concept to change how battles work but started playing a game and then paused it at some point and never got back to it. That's all I've played of Civ5. Over the past 4 - 5 years, haven't played anything of the Civ series. Been more focused on playing through games I've got for all my Nintendo systems. A few months back, I was listening to the Civ3 and 4 soundtracks on YouTube which gave me a big nostalgia for the games so I popped in Civ3 again which I have the most love for and played through that again. It was interesting going back to it since I was more use to Civ4 so there were certain actions and things I was trying to figure out how to do only to learn that the game didn't have them and the actions were a Civ4 feature. I was just playing for fun to remind myself of what the game was like and how it looked again but ended up having a really good start so I just kept playing and playing all through the ages.
Admittedly, it was just on warlord so the difficulty wasn't that great and by the end of the middle ages, I was the superior power and there just wasn't much threat to me. I stopped at the point I was invading the other major continent of the map and crushing their archers and medieval infantry with my bombers and tanks. I do enjoy blitzkrieging other nations like that in the end with either cavalry or tanks and taking multiple cities in a turn but the challenge is gone so victory is assured making it a bit harder to still care about the game. The experience has me contemplating playing a game of Civ4 as a refresher there and then finally giving Civ5 a shake.
Based on my experience, Civ3 would be a good starting point but with the changes that have been made since I say just dive into 5 or 6 and start learning with the current version. It would probably be faster than learning past versions and working your way up to the current iteration.