1080P is the low end of the spectrum these days and pretty easy to achieve.  I run mostly 1080P on my old rig:

Processor Information:
    CPU Vendor:  GenuineIntel
    CPU Brand:  Intel(R) Core(TM) i7-4790K CPU @ 4.00GHz  "Devil's Canyon"
    CPU Family:  0x6
    CPU Model:  0x3c
    CPU Stepping:  0x3
    CPU Type:  0x0
    Speed:  4080 Mhz
    8 logical processors
    4 physical processors
    HyperThreading:  Supported
    FCMOV:  Supported
    SSE2:  Supported
    SSE3:  Supported
    SSSE3:  Supported
    SSE4a:  Unsupported
    SSE41:  Supported
    SSE42:  Supported
    AES:  Supported
    AVX:  Supported
    AVX2:  Supported
    AVX512F:  Unsupported
    AVX512PF:  Unsupported
    AVX512ER:  Unsupported
    AVX512CD:  Unsupported
    AVX512VNNI:  Unsupported
    SHA:  Unsupported
    CMPXCHG16B:  Supported
    LAHF/SAHF:  Supported
    PrefetchW:  Unsupported

Operating System Version:
    Windows 10 (64 bit)
    NTFS:  Supported
    Crypto Provider Codes:  Supported 311 0x0 0x0 0x0

Video Card:
    Driver:  NVIDIA GeForce GTX 1070 Ti
    DirectX Driver Name:  nvldumd.dll
    Driver Version:  27.21.14.5148
    DirectX Driver Version:  27.21.14.5148
    Driver Date: 6 21 2020
    OpenGL Version: 4.6
    Desktop Color Depth: 32 bits per pixel
    Monitor Refresh Rate: 60 Hz
    DirectX Card: NVIDIA GeForce GTX 1070 Ti
    VendorID:  0x10de
    DeviceID:  0x1b82
    Revision:  0xa1
    Number of Monitors:  1
    Number of Logical Video Cards:  1
    No SLI or Crossfire Detected
    Primary Display Resolution:  1920 x 1080
    Desktop Resolution: 1920 x 1080
    Primary Display Size: 18.74" x 10.55" (21.50" diag)
                                            47.6cm x 26.8cm (54.6cm diag)
    Primary Bus: PCI Express 16x
    Primary VRAM: 8191 MB
    Supported MSAA Modes:  2x 4x 8x

Sound card:
    Audio device: Speakers (Sennheiser Main Audio

Memory:
    RAM:  16326 Mb

I mainly run games like Mount and Blade Bannerlord, Ark and a bunch of old stuff that are just old favorites.  Currently I don't really have a need to upgrade, as most new games don't appeal to me or will run on lower spec rigs like Mount and Blade.  But the new Nvidia 30 series cards have me daydreaming about building a new rig as they are a huge leap in performance.  But my processor would bottle-neck a new card of that caliber, so a complete system build would be necessary.  I would like to bump up to at least 1440P, but I don't really care about 4K and all that.

As for a low cost build, check out Paul's Hardware on YouTube.  He frequently does builds at various price points about every month so the tech stays pretty current.  PC Part Picker is a great site to do "virtual" builds and price out various builds to see how much it will cost and what is available.  It will also give you info on compatibility.  Tom's Hardware is also a good site for info and reviews.

Currently AMD seems to have the upper hand with processors as far as power and price, but Intel still has a lot of good processors that wouldn't break the bank at the power level you are looking at.  I do recommend going with a motherboard that is M.2 compatible and picking up at least one M.2 SSD as they are pretty cheap and very fast.  Some parts like power supplies are pretty hard to find these days with the slow-down in production due to Covid, so you may have to compromise there to get what you need.  Also, Win7 is no longer supported, so time to make the jump to Win10.

So, out of all the millions of computers out there still running XP, Microsoft singled you out to brick your computer?  Don't be silly.  Remember, there are a lot of business systems and programs that still run on XP and are not compatible with newer operating systems.  Our government has quite a lot of them.  But either way, Win10, as much as I dislike the layout of the menus, is a more stable operating system and boots much, much faster than XP or Win7.  Plus, Win10 is the only way to get DirectX12, which is geared for today's multicore processors.  DirectX11 and prior were made for single core or even 32 Bit systems.  I balked at upgrading to Win10 for a long time, but it was a free upgrade with my Win7 key code, it boots faster, I get more FPS in games and I can turn off all the "features" in Win10 that I don't want running, just like every other version of Windows.  Plus, I don't think you can even get drivers for newer graphics cards for the old OS'.  I think maybe the 10 Series cards were the last to offer drivers for Win7 and older?

As for Linux, I tried that as well but it was a huge hassle to get some programs to run and it was never reliable.  Some games were made for it, but many had weird problems and a lot of CTDs or just bricking the whole system.  I ran a dual boot for a little while with it and would compare it to Win7 and so many things ran butter smooth on Windows and then were a nightmare on Linux.  I think I would hate buying a new game to try and having to fight with my system for hours to be able to get it to run.  I only get to game on the weekends now, and I don't have time for that sort of thing.  Just my .02