Welcome to where PC gaming dominance truly began!
Where ISA/MCA/PCI/AGP had freed us from rigid one size fits all PCs at the cost of lots of money and strange forward, backward, and side compatibility. Where there are 5+ companies pumping out CPUs and they all fit in the same socket. Truly a magical land where you'd buy a new PC and it'd be not just old, but potentially obsolete in just 6 months time.
While there are lots of ways you can break down the eras of DOS, the way I saw it growing up is how I'll list it here. This is by no means comprehensive, pure DOS had a good decade and win9x nearly as long and the technology changed fast.
CGA:
4 color goodness that dominated the mid to late 80's.
Though with some clever usage of composite signal's faults, a psuedo "16" color mode can be achieved.
On a proper composite monitor, the resolution 'halves' and the overlapping lines create extra colors.
There was also tandy color which offered true 16 color.
EGA is very similar to this mode and also uses 16 colors, though the palette and format are a bit different.
VGA:
8-bit color hit DOS in the final year of the 80's and was the predominant mode throughout the remainder of the pre-win95. VGA was a game changer.
Became
DOOM:
Then comes Doom. Doom was the Crysis of it's day. True, Wolfenstien existed before it, but it was Doom that captured the imaginations of every PC, and non-PC owner. If you didn't have a PC, you bought one that you made sure could at least run it. While you could get the game running on the minimum 386 and VGA card, you really wanted a 486DX2 and everyone was eyeing the upcoming DX4 hungrily to really push the game full screen and as smoothly as possible.
DOS during the age of Windows:
DOS hung around as a gaming platform for a number of years even after windows 95. There are even 3D accelerated games for DOS using a voodoo/3DFX card. Games like Nascar Racing 2
(FAKE EDIT)
Over the course of waiting 2 weeks to get my 486 system up and running, I ended up with something a little beyond what I was expecting, and thus I'm extending this thread to include windows 9x gaming!
Windows 9x, 3DFX, and of course Direct X:
The reason I didn't intend on including this is because it opens up a whole new can of worms. Between windows 95 and 98, you actually cover all of DirectX gaming from 1.0 to 9.0c! For the sake of not filling this thread up with games that are only 10 years old, let's try and stick to DX8 and earlier!
This could literally fill an entire thread all it's own (and if someone ever wants to make a OT for Win9x, I'll gladly condense this back down to only being dos)
"Okay you convinced me! DOS and early Windows gaming looks great! How do I start today?"
The simplest way is to purchase these games on GOG. They come prepackaged with a preconfigured DosBox so they are as simple to run today as any other modern program and still configurable if you want to do some deep down dirty tweaking or if you want to try different graphics/audio modes.
The next simplest way would be to buy and/or dump your old games with an appropriate USB floppy disk or CD reader.
After that, we get in to the dark and dangerous world of real™ hardware. Real hardware can be a pretty scary rabbit hole. Early DOS machines will be unable to play many of the later games that require 386+ processors and a VGA card. Meanwhile, later machines (pentium and later especially, but even 486 at times) will run into problems with extended memory or the system simply being too fast or having too much cache leading to unplayably fast games. There ARE solutions to this with software like slomo and Throttle... but their compatibility can be hit or miss as well.
Much of the hardware is now also getting into 2-3 decades old. Power supplies and CMOS batteries are disintegrating and often taking their whole system with them. Worse yet, so many people viewed early computers as worthless that they threw them away or recycled them so finding an ideal system is starting to get expensive.
That said, if you are dead set on real hardware, I honestly recommend starting on laptops. Unlike full PCs, their power supplies are external and far less likely to have permanently damaged the system. There are down sides however since they are far less customizable and it's actually pretty rare to find a sound card in 486 and earlier machines. You also don't likely want one earlier than that as the screens are pretty terrible. Though more recently there are external sound cards that work for most games that use the printer port.
In general, it's still better to aim a little newer than a little older, and you might luck out and get a Pentium 1 or 2 laptop with a USB port, which will give you an easier way to transfer data than floppy or CD.
LGR has a decent video on the basics on choosing a dos machine.
Other Resources:
10 Greatest DOS games of all time
50 underappreciated DOS games
List of DOS commands
FreeDOS - MS and PC DOS replacement
THROTTLE - One of several tools useful for slowing your PC to play stubborn dos games.
Where ISA/MCA/PCI/AGP had freed us from rigid one size fits all PCs at the cost of lots of money and strange forward, backward, and side compatibility. Where there are 5+ companies pumping out CPUs and they all fit in the same socket. Truly a magical land where you'd buy a new PC and it'd be not just old, but potentially obsolete in just 6 months time.
While there are lots of ways you can break down the eras of DOS, the way I saw it growing up is how I'll list it here. This is by no means comprehensive, pure DOS had a good decade and win9x nearly as long and the technology changed fast.
CGA:
4 color goodness that dominated the mid to late 80's.
Though with some clever usage of composite signal's faults, a psuedo "16" color mode can be achieved.
On a proper composite monitor, the resolution 'halves' and the overlapping lines create extra colors.
There was also tandy color which offered true 16 color.
EGA is very similar to this mode and also uses 16 colors, though the palette and format are a bit different.
VGA:
8-bit color hit DOS in the final year of the 80's and was the predominant mode throughout the remainder of the pre-win95. VGA was a game changer.
Became
DOOM:
Then comes Doom. Doom was the Crysis of it's day. True, Wolfenstien existed before it, but it was Doom that captured the imaginations of every PC, and non-PC owner. If you didn't have a PC, you bought one that you made sure could at least run it. While you could get the game running on the minimum 386 and VGA card, you really wanted a 486DX2 and everyone was eyeing the upcoming DX4 hungrily to really push the game full screen and as smoothly as possible.
DOS during the age of Windows:
DOS hung around as a gaming platform for a number of years even after windows 95. There are even 3D accelerated games for DOS using a voodoo/3DFX card. Games like Nascar Racing 2
(FAKE EDIT)
Over the course of waiting 2 weeks to get my 486 system up and running, I ended up with something a little beyond what I was expecting, and thus I'm extending this thread to include windows 9x gaming!
Windows 9x, 3DFX, and of course Direct X:
The reason I didn't intend on including this is because it opens up a whole new can of worms. Between windows 95 and 98, you actually cover all of DirectX gaming from 1.0 to 9.0c! For the sake of not filling this thread up with games that are only 10 years old, let's try and stick to DX8 and earlier!
This could literally fill an entire thread all it's own (and if someone ever wants to make a OT for Win9x, I'll gladly condense this back down to only being dos)
"Okay you convinced me! DOS and early Windows gaming looks great! How do I start today?"
The simplest way is to purchase these games on GOG. They come prepackaged with a preconfigured DosBox so they are as simple to run today as any other modern program and still configurable if you want to do some deep down dirty tweaking or if you want to try different graphics/audio modes.
The next simplest way would be to buy and/or dump your old games with an appropriate USB floppy disk or CD reader.
After that, we get in to the dark and dangerous world of real™ hardware. Real hardware can be a pretty scary rabbit hole. Early DOS machines will be unable to play many of the later games that require 386+ processors and a VGA card. Meanwhile, later machines (pentium and later especially, but even 486 at times) will run into problems with extended memory or the system simply being too fast or having too much cache leading to unplayably fast games. There ARE solutions to this with software like slomo and Throttle... but their compatibility can be hit or miss as well.
Much of the hardware is now also getting into 2-3 decades old. Power supplies and CMOS batteries are disintegrating and often taking their whole system with them. Worse yet, so many people viewed early computers as worthless that they threw them away or recycled them so finding an ideal system is starting to get expensive.
That said, if you are dead set on real hardware, I honestly recommend starting on laptops. Unlike full PCs, their power supplies are external and far less likely to have permanently damaged the system. There are down sides however since they are far less customizable and it's actually pretty rare to find a sound card in 486 and earlier machines. You also don't likely want one earlier than that as the screens are pretty terrible. Though more recently there are external sound cards that work for most games that use the printer port.
In general, it's still better to aim a little newer than a little older, and you might luck out and get a Pentium 1 or 2 laptop with a USB port, which will give you an easier way to transfer data than floppy or CD.
LGR has a decent video on the basics on choosing a dos machine.
Other Resources:
10 Greatest DOS games of all time
50 underappreciated DOS games
List of DOS commands
FreeDOS - MS and PC DOS replacement
THROTTLE - One of several tools useful for slowing your PC to play stubborn dos games.