I’m a pretty big fan of SRPGs. They hit that sweet spot for me between RPGs and serious strategic games.
Any SRPG list is going to have Final Fantasy Tactics at the top. It wasn’t the first, but it was the first really big one with mainstream appeal and in many ways it’s yet to be topped. It’s big draw is in how much customization it allows. Characters can freely swap between classes (and there are a quite a few) and then mix and match the skills they learn opening up a whole bunch of different options. It’s not super well balanced, but usually the game is lenient enough that you can get through it with whatever combination interests you. The story is… a mixed bag. It starts off as an emotionally complex, morally gray story about an idealistic noble and his lowborn friend trying to balance loyalty, honor, and morality and then succumbs to its worst JRPG impulses and becomes a MacGuffin Hunt where you eventually kill god. It’s the kind of plot that seemed deep when I was a teenager and now just seems kinda dumb. Still, the gameplay really is top notch. It originally came out on the Playstation and got PSP and mobile ports more recently.
The series had a couple more entries on the Gameboy Advance and Nintendo DS, Final Fantasy Tactics Advanced and Final Fantasy Tactics A2: Grimoire of the Rift. They were much, much lighter story wise, trading the dark wartime politicking for much more lighthearted, cute adventure fare. FFTA is pretty skippable, in my opinion. FFTA2 is very solid, though, with good bite size gameplay suitable for a portable system. It plays pretty well when emulated on an Android tablet, I think.
Before Final Fantasy Tactics, there was Tactics Ogre. It came out originally on the Super Nintendo and got a port to the Playstation later. It’s much rougher than Final Fantasy Tactics, but it’s also a lot more consistent. There aren’t as many customization options, but you get more guys on the field and tactical placement matters more. Definitely harder than FFT, I would say. It has a pretty solid story too, in my opinion. It maintains thematic and tonal consistency, the main character has a solid arc, and it understands that MacGuffins are best used to motivate characters rather than interact with the plot directly. It got a remake on the PSP, Tactics Ogre: Let Us Cling Together which changes a whole lot and is generally better. It has some petty big flaws, but is still a great game which I would recommend highly. There was also a Gameboy Advance game, Tactics Ogre: The Knight of Lodis which was very good, but frustratingly slow to play. If you can tolerate very slow animations, there’s a very good experience in there.
The Disgaea series is the other big one. I’m not as keen on them as others. They focus a lot on grinding, and generally there’s not a whole lot of tactics or customization. You level up your guys and if your numbers are higher than the other guys you’ll win, more or less. The numbers scale up to pretty wacky extremes and by the end you’ll be doing millions of points of damage with every hit. If you want a game where you can just sort of chill out and grind a lot with plenty of anime style wackiness, they’re quite decent, though. The first one recently got a PC port available on Steam.
The Fire Emblem series is also very popular, but has never been my cup of tea. If you are interested in big strategic battles, though, it definitely worth a look.
XCOM: Enemy Unknown and XCOM 2 have, in my opinion, the best tactical gameplay. They can be very hard and very unforgiving, but they do a great job of giving the player an interesting set of tools to deal with situations. You get a whole bunch of neat abilities for your soldiers and when you succeed it feels like you earned it. Of course, they can also be very stressful when your favorite guys get mercilessly gunned down after because of a bad run of luck. The difficulty tends to spiral, though. If you’re doing well, the game gets easier and if you’re doing poorly it tends to get harder, hence the big divide between people saying they’re incredibly hard games and the people who say they’re pretty easy if you know what you’re doing. Regardless, they’re great.
Shadowrun Returns, Shadowrun: Dragonfall, and Shadowrun: Hong Kong are all solid singleplayer RPGs that have a similar cover based tactical combat feel. Dragonfall is generally regarded as the best, with Hong Kong running pretty close behind. Returns feel like a kind of practice run. It’s fine, but it’s completely linear and doesn’t really change regardless of the kind of character you play. If you think you’re going to play all of them, I’d start with returns because it would be hard to go back to it after playing the others. It’s fine to skip if you want to go straight to the better ones, though.
If you can tolerate 90s PC games interfaces, Jagged Alliance 2 is still pretty much the top of the heap when it comes to guys with guns tactical gameplay. You’re the leader of a mercenary company trying to topple a despotic regime. It mixes larger scale strategy with smaller tactical encounters. It still has a big following to this day and a popular mod that adds a whole bunch is still getting updates. The interface is very obtuse by modern standards, though, and could be a big turn off.
The Silent Storm games are a bit similar. You lead a squad of soldiers on missions in an alt-history WWII. Not super deep, but they’re mostly solid. The big appeal is that all the structures are very destructible. It can be quite neat to watch an entire building topple to a well placed explosive. They’re on the buggy, unpolished side, though.
There’s also the King’s Bounty series. There are a whole bunch of them and they’re more or less the same thing with different skins. You run around various world maps and recruit guys into your army while doing quests and whatnot. They’re pretty good, but can be very grindy. When you lose your soldiers you have to go and recruit replacements, which can get pretty tedious. Still, they’re solid.
Valkyria Chronicles is a pretty popular more recent game. It takes place in a fictional universe with a strong WWII vibe. You control a squad of soldiers with a weird turn-based/real-time hybrid system. Kinda hard to describe, you basically get an allotment of time for each action, and the world only reacts while you’re moving. It’s got a pretty big following and it received a PC port not too long ago.
A bit more esoteric, but Freedom Force and Freedom Force vs. The Third Reich scratch a similar itch. They’re PC games from the mid 2000s where you control a squad of silver age style superheroes. It’s not turn based, but pausable real-time. Being superheroes, your guys get odd mixes of various superpowers and the game mostly revolves around picking the right powers for each situation. It also lets you make your own heroes if you so desire.
Those are pretty much all of the good options I can think of.