I loved the hell out of *Everybody’s Gone to the Rapture *and Firewatch, both on PS4. Some deride those games as being ‘walking simulators’, but I loved them because I could get immersed in the story, the visuals, the voice acting. And I don’t get destroyed by 12 year olds with twitch reflexes that as an old guy, I just ain’t got.
The couple titles I mentioned I picked in part because they were newer and assumed your “new computer” had more punch in the graphics department. You might want to instead try Skyrim, Fallout 3 or Fallout: New Vegas in the “big open world to explore” department. They’re all excellent games but not as demanding on the system as Fallout 4 or Dragon Age: Inquisition.
One important note though is that both Skyrim and the Fallout titles have gore (as in you can literally shoot someone’s arm off, turn them to pieces, etc) so if that’s a deal breaker then maybe they’re not for you.
Maybe you’d enjoy Kingdoms of Amalur which was another “big world” type of RPG and, from what I recall, was relatively gore free. No exploding headshots, anyway. I don’t remember how twitchy or easy/hard the combat there was though.
Have you played Portal? It’s a first-person perspective game, and it looks like it requires twitchy reflexes, but in almost every case it doesn’t; if you’re trying to solve a level through lightning reflexes, you’re doing it wrong (with maybe one exception, where I could only figure out how to get past a certain point by contorting my body mid-air before I fell). It’s a wonderful puzzle of a game. And it’s the funniest game I’ve ever played.
I second the recommendation of Portal. One of the best games of the decade.
I just played through that a couple of months ago (that’s one off my “Looked interesting during a Steam Sale, never played” list…)
I played on Easy because I was more interested in the story. Combat options involve a fair amount of “pattern” following to get a lot of the bigger moves off that I found more frustrating than fun, but on Easy I was able to get through things pretty much with basic attacks.
If it’s not on sale now, it almost certainly will be during the Summer Sale, I think it took be about 70 hours to get through just about every quest, worth the $5 I paid.
Okay. So what I’ve got here so far is:
Not too much required in the way of reflexes
Some puzzling/solving is nice
Lots of options to explore
No blood/gore
Relatively low system requirements.
Let’s run with that. Here are some thoughts, all on Steam because I can’t bloody well remember what I have for the PS3 right now. x.x
FTL: Faster than Light; No reflexes required - stuff runs in realtime, but you can pause anytime you want for as long as you want. The whole game is basically a puzzle, and it has scads of options for you to combine. The graphics are nothing special, which is great because there’s no gore and the system requirements are super low. Roguelike, so no ‘story’ to speak of.
Legend of Heroes: Trails in the Sky; Classic JRPG style stuff. Heavy on the text and story, moderate customization, no reflexes, a light amount of puzzle stuff. No blood or gore. System requirements low.
Invisible Inc; No reflexes, purely turn based. Basically a puzzle game. Pretty good number of toys and options. Technically a little more visually violent than the other suggestions, but still very very little blood and death. Should not be a problem to run on a laptop GPU.
I played City of Heroes for several years. Loved it. Played WoW for maybe an hour total, and hated it, though I don’t know why, exactly.
If you might like to try another MMORPG, there’s always Star Wars: the Old Republic. It’s got a free-to-play option, so you can test it out before deciding whether to subscribe. It uses the WoW engine, so the controls should be at least slightly familiar for you. It takes place a few thousand years before the movies, so it’s kind of fun to pick up on some pieces of lore that you recognize from the film series.
Of course, if you’re not a Star Wars fan, you may not enjoy it as much.
Portal should be right in my wheelhouse, but I’ve watched my husband play a little bit and I just never developed any interest in trying it myself. I think it was a good suggestion, though!
You might like Gateways, an indie platformer that is sort of a 2D Portal.
You might look at Renowned Explorers: International Society. It’s obviously has exploration, it’s not reflexy, no gore, some role playing aspects, loads of strategy. Basically you lead a team of explores on exporation missions around the world looking for treasures and knowledge as you attempt to be the most famous explorer.
Thank you all for taking the time. I’m thrilled at your thoughtful suggestions.
Not sure about its graphics requirements, but Life Is Strange is one of the most amazing games I have played the last couple of years. Really great story line that you are affecting every time you do anything. It is available on Steam, with Episode 1 only costing $4.99. (There are 5 episodes total.)
Have you heard of Black Desert Online? It’s a MMORPG that’s as attacky as you like it. There’s a ton of different ways to earn money. You unlock skills through progression and you can be a tank.
Have you tried the Infamous series on playstation? It would definitly scratch your super hero itch. The first was my favorite.
Thanks for the new suggestions. I have not tried any of them, so onto the list they go!
So far, I’ve downloaded and started play of Gravity Ghost and The Room. I said I would let random.org pick for me, and that’s what I did. 
Enjoying myself so far.
You’ve heard of Minecraft, right?
I played very briefly but didn’t care for it.
Still playing “Gravity Ghost.” I finished “The Room,” which was interesting for the first half but didn’t really build to anything for me.
Just purchased “Life is Strange” and “Her Story.”
For only a yen, maybe just a pull or two off of a pachinko machine?