I have seen some lasers attached to the RepRap platform for cutting but most seem to be cutting paper, balsa wood, or merely etching. If I were wanting to build a platform for cutting wood, similar to the wood framed or boxed 3D printers on the market, what power laser would I need for that? I assume that a lower powered laser would have to travel slower but going too slow would add the possibility of catching the wood on fire (not good).
Please do not go down this road. First, not all lasers are equally absorbed by the material and the energy converted to heat to vaporize the material. The light not absorbed is reflected right back into your eyes. This is especially dangerous because it doesn't make you go blind instantly, fooling you into thinking there is no harm. You got the other part right, the lower the laser power, the less turned to heat, the longer it takes to cut, the longer you risk exposure to your eyes. That's right, a low powered laser is MORE dangerous than a big one. Next, the only way to properly cut is with air assist. This means a stream of air blows away the vaporized material so the laser can keep cutting deeper. This also prevents fires. The thing we haven't even touched is a proper safety enclosure, proper bed design to not reflect the laser beam back into the laser killing it and your eyes, and finally smoke/particle exhaust.
Simply put, these cheapo DIY lasers are dangerous, and are also illegal.