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.
Strapping a laser to a cheap robot made with flammable plastic parts and no enclosure is stupid in the extreme. Don't do it. Seriously, just don't. RepRaps are not suitable for laser conversions.
You have to worry about reflected light damaging your eyes, and for the blue diode lasers currently growing in popularity, causing skin melanomas. You have to worry about mechanical vibration from jerky motion loosening fasteners. You have to worry about the workpiece catching on fire. You have to worry about the fumes being generated from etching and cutting. You have to worry about firmware freezes locking the laser on. It's dangerous to you, anybody in line of sight of the machine, and your property.
Many of the lasers currently being sold for RepRap conversions, particularly from Russia, violate US and EU safety regulations related to power and safety interlocks and should not be on the market at all.
The people posting videos of their RepRap laser conversions are almost always ignorant of proper laser safety requirements and regulations. It's downright scary how much blue flare you can see the camera picking up in a lot of these videos. Don't follow in those people's footsteps.
More directly answering the question details, most people doing light etching or paper cutting type work are using small 0.5-2W diode lasers. These are particularly dangerous because they have poor focus and because they don't have the power to cut cleanly and quickly. That means more fumes, more fire risk, and more damage to the workpiece from edge charring.
Slowing down the laser is not a good solution: dwell time is your enemy. You want a beam powerful enough to near-instantly vaporize the material, not slowly burn it away.
An entry-level proper lasercutter for cutting things like plywood and acrylic is more likely to use a 40w CO2 laser. It should have air assist and fume extraction, and a safety-interlocked enclosure that 100% reflects or absorbs the CO2 laser light wavelength. That basically means a dedicated machine.