I agree with the consensus: PC. With emulator software, you can play almost all old console games for free. You can also play most all old PC games (and a lot of new ones) for free or negligible cost via GOG and Steam sales. I suspect you’d find most of your top 10 list on GOG, DRM free, for a couple $ each.
If you do like console-style action games, you can use a controller with your PC. Plus you have options of mouse + keyboard, joystick / flightstick, wheel and pedals, etc. etc. for other types of games. (the Saitek x52 flightstick was great for MechWarrior games!) One of console’s worst drawbacks is the miserably limited UI options - 2 thumbs for everything.
Re: hardware - I have an old Core2 Quad 2.40GHz with an NVIDIA GeForce GTX 560 Ti. I think that’s decade-old tech (bought it used cheap). I’ve just finally begun to hit the limit where new games don’t run well at max settings. Fallout 4 doesn’t do well
But that’s because of the RAM (motherboard is limited to 4GB). There was one other game I tried that didn’t do well (again because of RAM - too much disk swapping).
I have looked at upgrading, and as the others have said, it sounds like an i5 (or maybe a recent i3) with 16GB of RAM (or more) would be the way I’d go. I could use any modern video card because for the games I prefer, even my old one does fine at high settings. That might be different depending on the games you like.
I don’t really have a top 10, but to give an idea of the things I like:
Fallouts: 1, 2, 3, New Vegas (and hopefully 4 once I get an upgrade)
4X’s: Civilizations, Alpha Centauri, Master of Orion 1/2, Space Empires IV
Wargames: Gary Grigsby’s World At War, Advanced Tactics Gold, Decisive Campaigns, Strategic Command - European Theater, Field of Glory, Harpoon Ultimate Commander’s Edition, Combat Mission
Strategy: Europa Universalis series, Warlords II
Sub Sims: Dangerous Waters, Sub Command, 688i Hunter Killer, Silent Hunter IV, Fast Attack
Driving: Burnouts, FlatOuts
RPG/Roguelike (other than Fallout): Baldurs Gate, Temple of Elemental Evil, Titans of Steel, Ancient Domains of Mystery, Decker
Economic: Capitalism Labs, Wall $treet Raider
RTS: Old Command & Conquers, Warhammer 40,000: Dawn of Wars, 8-Bit Armies
other: Lately, I’ve been trying out weird new indie games and adventure games; used to love flight sims (F-19/F-117, F-22) but haven’t tried any lately; FPS are mostly in the past for me, but I might fire up the Crysis games again; have a ton of games I haven’t even played yet
So my take on it may be a bit different than others. If you like open-world games, you’ll want more RAM than I have. Modern CPUs are more than up to the task (at least in the intel i# line). Graphics cards have been more than up to the task (for what I like) for over a decade. There are more games than I’ll ever have time to play. A new gaming PC for me would probably be cheaper than a console.
(My last PC was a newer i7 with 8GB RAM, but it never got near capacity when gaming. I did overheat it, but only after playing several hours when it was over 100° in the room. This $250 one performs at least as well as that $1200 one did, although that one would probably do better with modern open-worlds due to the RAM.)