As for the grout, I keep hearing about this product - Finazzle. I've never tried it but people seem to be impressed.

I too have used a toothbrush or or small scrub brush (lasts longer) with grout cleaner. Comet Gel cleaner with Bleach works good too. You must rinse either product.

Get your tile good and clean before tackling the grout

Now, you don't want to use this as the standard way to keep them clean. Harsh chemicals WILL destroy your grout sooner than later. However, (for me) this was a really good way to just get the worst taken care of the first time, and then it's up to me to be careful to take care of the floors better than previous owners did.

Also, I used the bleach pen because I had one around & hardly ever used it for anything else...and they're not cheap. 1 bleach pen went around maybe 15 tiles and that's it (but that was about the right size of the area I wanted to focus on). If I ever had to do this again, I would look into comet or oxyclean and old-fashioned scrubbing.