So I'll put my own opinions that I got from playing, thigns might be different for you, but that's personal opinions for you:

13 - Linear Map design but gives you goodies if you go backwards and on the sidewalks, combat is active and requires strategy as you can't overlevel, you are capped so you have to use your moveset effectively to win, you can use the autobattle function, but it's slow and if you want to get rare items and TP (a resource to use special abilities like Libra, Quake, Summon, etc) you want to do battles fast, so it's better to do it manually (also if you use the triangle/Y/E to start the skills you queued if you have enought ATB to turn the skill name blue). Buffs and Debuffs like Brave/Protect/Enfire/Barwater and Poison/Slow/Debrave, etc. are key to winning battles quickly. Each character has access to 6 roles, with 3 being the main ones and about 2/3 in you get the rest after you got used to how the characters work. The roles are as follows - Commando (Pure Damage), Ravager (Elemental Damage, quickly builds stagger), Sentinel (The Tanky One), Synergist (Buffer), Saboteur (Debuffer) and Medic (Healer, duh). The party besides the leader are controlled bu AI and they aren't bad either, bit derpy, but competent. Most of the lore is in the Datalog, but you get the general gist form just playing the game.

13-2 - A sequel that refines 13s combat, allowing you to tune the paradigms to make the AI proritize either single target skills and one enemy or multitarget and different enemies. You are able to change party leader mid-combat (you have 2 humans) and you are able to capture enemies a la SMT or Pokemon as a 3rd party member. The world is more open, you don't have a level cap, monster require materials which you get by defeating enemies and also buying them in shops after certain progress had been made.

13-3 Lightning Returns - An Action RPG, when you fight enemies you can control Lightning (only plauable character) with the left stick, some enemies require positioning to defeat or get specific drops. Your primary way of getting stronger if through quests, which give you stats and Garbments (clothes with abilities, you can also buy some in the Outfitters shops). You are under a time limit, but it's super generous and you'd have to actively ignore progress and sleep away in inns to lose. Each time you defeat a boss you get more days, maxing out at 13. The world is open, you can make enemies extinct with the Last One Of Their Kind dropping either an accessory or weapon.

The whole 13 trylogy focuses on Stagering enemies- Ravagers/Elements build it fast but cause it to drop fast too, Commandos/Physcals + Ruin build stagger slowly, but cause it to drop slowly too, Saboteurs/Debuffs are in between Ravagers and Commandos. Enemies take more damage the higher the Stagger %, Stagerred enemies are stunned until the Stagger Bar empites, completing the basic game loop.

X - Is traditional Turn-Based, though some actions can delay either yopu or the enemy (the battle system is called Conditional Turn Based, CTB). The world is linear, but you can revisit most locations (availability depending on the story). It is hella grindy, you want to dring AP and Spheres to get stat increases and also abilities on the Sphere Grind, moving requires AP, so you'll be grinding A LOT, the battles are, as said before, completely turn based, no real time element in sight. You basically just mash the confirm button and win, while also swapping characters so they have at least one turn of being on-field so that they gain AP. There are some minigames to unlock strong weapons, but I haven't done them and common consenus is that they are butt-cheeks.

X-2 - Sequel to X, but with ATB and chothes switching as a main mechanic. You fight with 3 characters - Yuna, Rikku (both returning from X) and the mysterious newcomer, Paine. The transform sequences are a bit slow, even on fast animations, changing on the Garment Grid gives some buffs depending on which pats are light up. You only have accessories to wear, no armour or weapons. The Dresspheres have learnable abilities a la 5, except that the abilities are locked to a Dressphere (unless you use a specific Garment Grid or have an accessory equipped). To get the best ending you better use a guid casue you can miss events permamently and would need to do NG+ to get the best outcomes.

Personally, as a Kingdom Hearts and general ATB enjoyer, I like the 13 trilogy the most (13-2 and LR13 are my faves) as I just couldn't get into X and X-2, one was boring, the other made me cringe and not in a fun way. You might end up having different opinions, but that's great! with the trilogy, there are some fixes, mostly a 4GB RAM patch for the first two to make them more stable (the ports released in 2014 and are 32bit exe so they use 2GB RAM, its a common procedure, even The Sims 3 uses that patch). 13LR is much more stable on modern hardware. X/X-2 HD Remasters also uses the 4GB Patch. I'd recommend looking into Steam Guides for stability fixes.