I never actually made a list of the mods, but let me see what I can think up. Keep in mind I haven't actually play-tested most of the mods I have seen.
I'd definitely recommend Luke's UFOs, and I have used that mod. It adds more UFO variants without changing anything important about the game. My mod is actually intended to run with it, I was going to integrate it but haven't got around to it. Just put Luke's UFOs higher on the list than any other important mods in the list because it declares a bunch of redundant vanilla attributes which might otherwise override your other mods. Apparently higher on the list means lower priority.
Luke's UFOs forum linkAwesomeguns is a good mod I think. I haven't actually installed it directly, but I've used plenty of the artwork from it. As I understand it, the mod primarily updates the weapons to look and sound better, but also adds a few of the community-standard weapons to expand the arsenal, especially in the beginning of the game. A lot of mods do this, adding things absent from the original game such as machineguns, submachineguns, shotguns, sniper rifles, and more. It gives you more choices without really changing the overall game. Some mods may have overlapping weapons--you might get two or more weapons that are very similar but not quite the same.
Awesomeguns forum linkAwesomeguns' awesome github pageIt's actually difficult to browse mods without the mod portal. The forum doesn't sort them into categories. Well in general, the kind of mods I would recommend are basically things that add quality of life features or expand your options. I would potentially recommend things that change the balance if they are claiming it is to resolve balance problems in the original. Now if you play with my mod or any other major balance fix mod, it'll be intended to run by itself so you won't need to install any other mods--so it's just a matter of choice on your part. But all the major feature mods that change the game drastically are best experienced after playing the base game, or so I feel.
Here's some of the biggest mods changing the gameplay and story:
From the Apocalypse
X-Com Files
XOps
X-PiratesThese mods are excellent, but they are total conversion mods, meaning you play with only that mod installed as well as any optional mods provided with it. They are also geared toward veteran players. I would definitely give them a try later if you like the vanilla game, or now if you like to punish yourself.
I'd like to mention Final Mod Pack here. It is a mod compilation containing all of the community favorites, with a lot of work put into making them work together. It doesn't contain individual standalone mods, but rather acts as a single total conversion mod. You can play it like it is and experience heavily-modded gameplay, or you can look inside the folders and find out what mods were put into it. If you want to find more mods, FMP is a good place to look for inspiration. Many of these mods can be found on the forum, however a lot of them are only posted on the deprecated mod portal so you might not be able to access them.
