I used a StoneTec sealer, one of their enhancing sealers on some granite tile. The granite I used (Kashmir white) does absorb water, and the sealer makes it look almost like it is wet - it does enhance the colors, bringing out the black specs and the garnet. Aquamix makes some good stuff. I've not had good luck with some of the Tilelab stuff, but they may make a decent one.
You can order the StoneTec stuff at the store on
www.johnbridge.com. You may find it locally.
Depending on the brand of sealer, follow their instructions. You need to wait at least a little bit before sealing to allow the tile and grout to dry. Then, depending on the sealer, you may have to wait again before you can take a shower...this is very much specific to what you use, but they all want you to wait a little.
Epoxy grout is nice in that it does not need a sealer and resists stains and buildups of soap and crud. It does cost about 4-5x more in materials than regular grout, and is (only a little) harder to clean up after, but - it does require a different cleanup technique. If you don't follow the instructions, it is a MAJOR BEAR to clean up later.
WIth the tumbled travertine, when grouting, the usual procedure is to fill the depressions and holes. You can wash some of the grout out, but any deep holes should be filled, as otherwise, it is a maintenance pain to keep accumulations of crud out of those holes.