The laser diode that you linked to is the read diode, not the write diode. Read diodes are (typically) Red, and are generally terrible for even low power laser pointers. It does, however have supreme consistency, and is a very clean beam.
Most DVD writers use a 405nm Violet laser to burn discs. 405nm lasers are excellent for engraving, as they are easily the most focus-able wavelength of laser you'll find on the market today.
Power is another concern. Especially with the 405nm lasers, you NEED eye protection. So long as you aren't looking at the dot directly, you will not damage your eyes (but accidentally looking at dot is possible). However, you will need the protection to focus the dot. Generally, you will want something that can be used consistently without overheating as far as power goes.
- At 120mW you can burn Items, and the engraving will easily come clean off.
- At 300mW you can start engraving non-black objects, and the engraving is somewhat texturable, and you can barely feel it.
- At 500mW you will need to put 3 INDEPENDENT safety mechanisms on your engraver for it to be legal in the UK and US. you'll have a wide range of things that you can engrave onto at this power level, you may want to have a fan running to cool the material.
- At 1000mW, you're at the higher end of the 405nm spectrum, and is probably your best bet for making a laser engraver. Just wear eye protection, for the love of all that is your eyes. This will engrave close to any material, including unpolished metals, but not glass. Exceptional cooling is needed for this type of diode.
Best of luck!