Here's a list of the parts I'm planning to use.
2 stepper motors for XY control (0€, from old printers / scanners)
Mechanical structure for the XY table (0€, I'm planning to use printer & scanner parts)
Red laser diode 150mW - 250mW 650nm (0€, from an old 16X DVD burner)
Laser module with focusable lens ($9.50 from AiXiz)
This is needed to collimate the laser beam. I don't know what that means either, I just read it off some other tutorial page! I ordered the 650nm 5.0mW 12x30mm module with a glass lens as an accessory. Normally they come with plastic lenses. Sounds bad having a plastic lens on an engraving machine that's supposed to burn stuff.
Laser diode driver circuit (?€, parts list later)
Arduino (20€ from your nearest Arduino dealer)
To control the stepper motors. I will use Arduino for this project because of the ease of use and available libraries. I have one already.
Adafruit motor shield for Arduino (?€ from nearest Adafruit dealer)
This one is needed to power the motors. Arduino itself cannot power the motors, the motors need another power supply and some driving circuitry. I want to get engraving as fast as possible so I don't want to waste time making my own PCBs. This kit seems perfect for me.
Computer to send control data to Arduino.
Control program on the computer that eventually controls the whole thing
I'll code it when the hardware is ready.
Cables, screws, tools, power supplies, whatever.
This list will be updated later when things clear up.