To play old pokemon game you just need a Gameboy, any product labeled "Gameboy" that isn't the Gameboy Micro will suit your purposes. If you need a new one, your best options are the following:
Game Boy Color (not recommended)
There's no reason to get a gameboy pocket (or, barf, an original gameboy) since the GBC can easily emulate the monochrome display if you MUST not have color. Otherwise, the GBC allows gen 2 to be played in proper color as well as lending a less-impressive splash of color to the original games.
Also the GBC can easily trade via link cable to other gen 1 games, assuming you have friends to trade with (pretty unlikely these days).
Game Boy Advance SP (recommended)
Might be a bit more expensive, but the first built-in backlit and has rechargable batteries. Most people forget that old gameboys had disposable batteries and non-backlit screens. Only potential negatives are a possible cost increase compared to older models, and the GBA SP isn't quite as comfortable for extended use--I've only found this to be a problem with "twitch" games like Mega Man, shouldn't be an issue for Pokemon.
There are apparently "universal" link cables that let you attach a GBA to a GBC for trading like gen 1&2 require but I haven't used such hardware.
I know this isn't the question, but take heed that old gen pokemon games really don't hold up as well as you might hope. The PC box system was AWFUL in gen 1 and still poor in gen 2. I highly recommend going for the gen 1 and gen 2 remakes personally, they're available on GBA and DS respectively (FireRed and LeafGreen for gen 1), so a single DS system would be enough to play both of them, and all following generations up to 5.
After you got me interested, I did some research.
Apparently, it was distributed through a machine called the Mew Machine (Celebi in Generation II):
A person has posted on a forum about this machine, and his speculations are as follows:
I got a feeling that there are 2 Super Famicom's inside aswell as 2 Super Game Boy 2's that are linked with eachother.. but I'm not quite sure about the rest. Besides the monitor...
I'm afraid I can't find any concrete/official sources on this, but it seems like you were right about how it was controlled!
Additionally, I've found some sources stating that the Mew was simply traded (as I originally seemed to remember) in some regions. This was done using a "special" gameboy and game version, loaded with several level 5 Mews. It appears to be a regular gameboy with Pokémon Blue, though somehow modified or loaded with the Mews.
Best Answer
I got the games today, and can confirm that none of the glitches have been fixed.
The games really are true to the originals.
It is still unclear however whether you will be able to upload these glitched Pokemon into Pokemon Bank.