Slonk

I'm no expert - all my info has come from readin message boards like this but I'm in a similar situation to you. We already have some of the same tiles that my Mum bought ages ago, and gather that they defintely need to be filled with grout or caulk (if that's the right word) - grout is preferable but more time consuming. Unfilled will gather dirt and mould. If you can get filled an honed that would probably be the best option for you.
If it's unpolished (honed), any etch marks from acids spilt on it will be less visible. Polished travertine in a kitchen sounds like it will get damaged more visibly. Honed travertinewill be less likely to etch from things like lemon juice, vinegar etc.
Tha's what I have gathered whilst doing my research, but anyone feel free to correct me.