I'll break it down by my own personal preference, just based on ease of use and modern UI amenities.
Civ II
Probably a nostalgia choice. The music is a bit archaic by today's standards and especially modern Civ standards in particular, but that's really the only major downside, aside from getting a copy to work under modern OS'. The game itself is fairly straightforward. Manage your settlements into cities, build wonders for bonuses, amass a great army to conquer your rivals, ally with them, or simply become such a massive technological powerhouse that you beat everyone to space. Of particular note is a few annoying things like late game spy spam from the AI, a few cheaty things and of course, a UI circa Windows 3.11/95 era. I enjoyed getting a pimpin' palace and of course, who could forget the advisory council?
Civ 4
I feel like this is that last pure Civ that Firaxis didn't attempt to really mainstream into a boring mess. It was the first version to really embracing the modding scene, felt complete and felt like it handled everything I hated about 3 in a far better way, or outright removed bad mechanics from that game. It also has the Colonization pack for those of you who are interested. (Although, I still prefer Freecol or the original, despite its age.) I feel this is probably one of the better modern iterations and is worth a purchase, especially if it's on sale.
Civ 5
I actually really enjoyed this, after patching and all DLCs were put into one package. I've probably logged hundreds of hours into great and unique mods, both for adding new factions, or total conversion mods like the Lord of the Rings versions. The modding scene is probably what really makes this game stand out for me, personally. There's everything from Fallout mods and maps for them, the inclusion of all or most of the factions, (BoS, Legion, NCR, Enclave, New Vegas, etc.) They come with unique abilities and units. There's an elder scrolls mod that includes a full map of Tamriel, with most of the factions and races, a Game of Thrones mod with all the houses and a custom Westeros map, along with total conversion mods that completely change the mechanics and maps. As for the core game itself? Yes, it has annoying things like one unit per hex, causing massive movement spam when you're on the march, there were the early nuke 'em Ghandi bugs, and a few other annoying aspects, all of which can be modded out or modified, should you wish. City building felt rewarding and fun, but I will say this, where the game ultimately falls short? The AI. It doesn't matter how benevolent you are, once you've gained a massive disparity in power against the other civs? They start slandering you, become aggressive, demanding and ultimately leads you to simply conquering them out of irritation. There's a good variety of Civs here after DLC, with some being more OP in aspects than others. (Babylon tech rush?) I'd recommend on sale, in a complete package. The still active mod scene alone is more than worth it, imo.
Civ 6
One thing I will warn. It does have Red Shell, and I can't remember if they pledged to remove it or not. If that is a deal breaker for you, simple ignore this entire portion of my post. I can't blame you.
That said, there's good and bad here. The art change is a bit jarring, but the tech trees, unique way of building cities that are each their own style based on your needs is a nice upgrade. The 3 (or 4, depending on wonders) use worker unit limit is actually a good way to remove wasted time between turns watching swarms of workers move about on their automated duties. (Some may feel this is a negative, as the worker swarms can give a deeper feeling of a massive empire constantly building, upgrading, etc.) I personally don't have a strong feeling either way. Spies are handled differently, and units actually upgrade in newer and unique ways, aside from stats changes, unlocking unit specific abilities like bonuses to ranged, bonuses against ranged, bonuses when sieging, attacking not costing movement, etc. There's a large diversity of civs here, each with their own unique way of improvement and expansion. The modding scene hasn't quite caught up to 5's and with the huge backlash over the Red Shell issue, it may not. It's tough to say. If that doesn't bother you, I wouldn't recommend a full price purchase, but a playthrough if you can get it complete and on sale might be worth it.
Civ 1
I rank it here simply because of its status as progenitor and historical curiosity. Frankly, it's borderline unplayable by modern standards. Even MoM's ancient UI is still serviceable and easy to eventually get the hang of, as well as being easier to understand mechanically. Without documentation, the UI is way too antediluvian to put up with, and the same goes for the mechanics. I mean, it might be worth a pick up during deep discount just for collection's sake, but I can't recommend the game itself, unless you're a masochist.
Civ 3
Hated it. Hated almost absolutely everything about it. I hated the cheating AI, I hated the penalties for expanding your empire, I hated the shitty way it handled strategic resources, (which 4,5 and 6 do a much better job of managing.) It just was not fun for me. If a game starts to feel like work or a chore, it's no longer game, or at least, it's no longer entertainment, which is why I play games. I would recommend a solid avoid.