At the small size you're intending the pieces to be I think the answer to this is simple and it doesn't revolve around any conventional tools or shaping operations, not with wood's inherent friability and the potential losses from errant chip-out at edges.
I'm sure that's the way to do these, not only will the accuracy be far higher than they could possibly be made by hand (not just by you, by any human) it means that no marking out whatsoever will be needed.
Laser cutting will require that a digital outline file be prepared, but once this is done the cutting is trivial (fully automatic) and at any point in the future further tiles can be made, e.g. to replace damaged or broken ones, by running the same file again.
These outline files can be of a few different file formats, generated by different programs. Ffor example a .AI file from Adobe illustrator, a .CDR file from CorelDRAW or a .DXF file from AutoCad. In addition, laser-cutting services will give further details to help you lay out the outlines on the sheet properly, e.g. providing a sufficient border around all sides of the material.
If you hadn't given particular though to materials yet, particularly if the tiles are intended to be quite thin I think you should probably go with a high-end plywood rather than solid wood. There will be some sticker shock with quality plywood, but it will be worth it for the quality hardwood face veneer and the consistent, void-free internal plies.
If you do want to go with solid wood a close-grained hardwood should be chosen, not something open-grained (e.g. oak or ash) and certainly not most of the softwoods, which have very variable hardness from the light 'earlywood' to the darker 'latewood' bands. An ideal choice would be boxwood, which has grain so fine it can be nearly impossible to see with the naked eye. It's also very hard and dense, hence why it was the wood of choice for small, accurate rules (rulers). But boxwood could prove very hard for you to get in the amounts you need and possibly the price will be too high anyway.