Ok, great...I see two issues: the sealing - and the little holes and indentations in unfilled travertine.
First, as far as sealing is concerned, know that travertine, in general, is quite dense and will not, normally accept much sealer. However, the harder travertines are very good at accepting a polish and therefore are polished and sold as such. The softer travertines (ones that do not take a polish very well) are sold as tumbled, or for outdoor use. These travertines are relatively 'soft' (compared to other travertines) and therefore could possibly take a impregnating sealer. Since it's a bit of a toss-up and you're sealing other things, go ahead and seal it. But only once and make sure there are no puddles left on top.
But the larger issue IMO, is the unfillled part; as you can imagine, over time these holes will become filled with dirt. This may or may not appeal to you as you'll probably wonder where that nice new look has gone. Tumbled travertine can be filled - but it may be a bit late now. Just be aware of that fact. Some good grout restoration contractors (like us, he-he) can take care of that but there's no solving the main issue unless the holes are filled.
The relatively good news is that some etches will not really appear as etches at all...so you're saving the costs of repolishing, in a way.
I'm not one to recommend brand names, just ask a stone supplier for an impregnating sealer...they'll have what you need. My guy (the biggest stone supplier in my city) sells Lithofin products and I like them, but that's a personal choice.
As for cleaning, use products that are intended for stone. Not the best Mr Clean, or Ajaxs of the consumer world...neutral cleaners are out there that are formulated for stone. That's what you need.