W/O knowing the brand or type of tile you have, as for the joints, sanded and unsanded joints should be sealed. Natural/Clear grout sealers may change the color of the tile for a few days but after that, the natural color should return. Sealing will help maintain the life of the joints but not necessarily the life of the tile.
There are lots of sealants on the market these days. They even come in a variety of application-methods. One that might suite you because of how much you have to do comes with an applicator tip. I've got a few links for you to peruse. Before you buy your sealant, DO read the instructions. Look for things like 'clear', 'natural', 'penetrating', 'wont change the color', etc., etc.. As for why you've seen discolored grout at other homes can be from a number of factors. 1) The homeowner didn't clean the grout before sealing, therefore, dirt got sealed in. 2) The grout discolored on its own over time. 3) If it gets a lot of sunlight, it may discolor. 4) A cheap sealant was used.