People often like and want small grout lines on polished stone tile to make it look more monolithic (like a slab). The smaller the grout line, the greater any flaws in the install show. The flatter the surface, the easier it is to make it look good.
First, stone, especially travertine which can have more internal flaws than some other stones, requires a subfloor twice as stiff as one for ceramic. On an older house, the joists are rarely set up for this. Then, the subfloor for a stone install requires two layers of ply, ideally the first 3/4" T&G, and the second at least 3/8". Each must be C faces or better on both sides and with exposure I (waterproof) glues. There's rules on how the second layer needs to be installed.
For great tile help, try www.johnbridge.com. They have a deflection calculator and a lot of help to determine if what you have will work, or if not, how to tweak it so it will.