Just get one of those "splat mats" from Babies R Us (or for the downscale version, get a plastic painting drop cloth at Home Depot and cut it to size!). Put it under the high chair to catch the mess, then rinse it off in the sink afterward. Problem solved!
To answer your specific question about cleaning hardwood, I have never found anything better than a basic cotton mop and Pine Sol, and I've had hardwood floors as long as I can remember and in many different houses. But that's a pain to do 3 times per day. Definitely go with a splat mat.