Run what you download.
Downloading a 1983 binary is only half the fun. These are the emulators worth using for the platforms in the library — hand picked, not user uploaded, so they skip the queue entirely.
Each one links to its own official download page. We point at the real thing rather than rehosting someone else's build, so you always get the current version from the people who make it.
AppleWin
for Apple II Plus
The one everybody uses for the Apple II line. Emulates the II, II Plus and IIe, disk II drives, the lot.
Getting going: Grab the latest release zip, unpack it anywhere, run AppleWin.exe. Set the machine to Apple II Plus, then drag a .dsk straight onto the window to boot it.
Altirra
for Atari 800XL
Frighteningly accurate 8 bit Atari emulator. 800XL, 130XE and friends, down to the cycle.
Getting going: Unpack and run Altirra.exe (no installer). System, choose 800XL. It ships with built in kernel replacements, so it boots with no ROM files; point it at real ROMs under System, Firmware if you have them.
DOSBox-X
for 8086/PC
DOSBox with the sharp edges kept on: real 8088/286 cycle targets, more video hardware and better disk support than plain DOSBox.
Getting going: Install, then MOUNT C C:\somewhere to give DOS a drive and run your binary. For period correct speed set cputype=8086 and cycles=315 in the config.