I have never lived with (owned) travertine floors but in Texas my kitchen had porcelain tiles and I hated them because they were hard on the feet/back, cold (which some would say is a blessing in TX but the a/c was usually on too so that was not needed in my opinion) and worst of all, they were slippery if wet or I dropped something on them. And the grout ... ick .. was always filthy no matter what I did to clean it. I dropped a bottle of balsamic vinegar right in front of the stove and when I went to sell the house, I had to scrape a LOT of grout out and replace it because anything like that seeps right down and cannot be washed out/off.
Travertine might be better I guess since I think the 'slabs' are usually larger than a standard tile might be (meaning fewer grout lines - and I think thinner ones as well) but what about the 'slippery' factor?
In NC my kitchen floor was sheet linoleum (I picked it because of its great natural properties) and I loved it. Warm, easy to clean, water-resistant, environmentally sound, long lasting, colourful, and easy on the back/feet. It was not cheap but I think it was a good choice - and I think it could work even in a commercial kitchen (if that is allowable by the authorities?)
p.s. I am drooling over that Big Chill stove! Looks as though that is a wonderful choice for you.
