You'll use a little more, but forget just trying to put sealer on just the grout - wipe it entirely over the tile. The magic key point to remember is you MUST buff off the sealer on the tile before it dries, or you will end up with streaks. A little more sealer will help disolve it and let you clean it off, but don't wait too long.
There are all sorts of sealers..both water based and oil based. A good sealer can cost over $100/gallon. The good thing is you don't actually use much. Depending on use, you may only have to do it once every few years. A sealer will not prevent moisture from penetrating, but it will slow things down, help prevent oils from penetrating and soap scum. Avoid the cheaper ones from the big box stores. StoneTech and AquaMix both make some good ones.
Trying to keep white grout white will be a challenge, and you'll probably lose. Sealer will slow that down. Next time, consider an epoxy grout. Costs a lot more for materials, though.