I never actually played any of these games. I remember hearing about them. How many are there?
You should fix that. Now.
There's 5 not counting this one:
Secret of Monkey Island - 1990 (remastered with new artwork in 2009)
Monkey Island 2: LeChuck's Revenge - 1991 (remastered with new artwork in 2010)
Curse of Monkey Island - 1997
Escape From Monkey Island - 2000
Tales of Monkey Island - 2009 (this was developed by Telltale and is episodic)
They're all amazing, funny and definitely worth playing. The remasters have a button to go between the remaster and the old DOS version (which you can otherwise get free on abandonware sites); the remasters have voices.
COMI (3) is easily the best and most memorable one. Escape is worth playing, but they tried doing 3D and missed the mark a little. Tales was quite good, and had some loose ends that I'm hoping Return will close. You can get everything on Steam and GOG.
You also don't necessarily have to play them in order, they can all stand alone. There are characters that appear across some and all of them. But each game definitely references the previous one.
If I had to rank them:
1. Curse of Monkey Island
2. Tales of Monkey Island
3. Monkey Island 2
4. Monkey Island 1
5. Escape from Monkey Island