Hi Jose,
- "great detail and therefore accuracy" would require an expensive machine. "budget friendly machine for home use" is not going to produce the fine results you are asking for.
- "either plywood or some sort of metal like brass or steel" - Different machines are used for wood and metal. There are some combo options but they are very expensive.
- "Is it possible to engrave on such a thin piece of material?" - Absolutely.
- "Is there a reliable online company I could perhaps outsource this to?" - There are many. Look for CO2 Marking machine for wood and Fiber Marking machine for metal.