JLM is correct, you aren't going to win the battle to keep your carpet clean by keeping the tile clean. There's fine particulate matter than evades the best cleaning intentions. We use a top of the line "hepa" Miehle vacuum cleaner and then follow up with the "Woodpecker" hardwood floor cleaner system. It is astounding how much fine dirt remains behind after a thorough vacuuming with a good vacuum with a rotating brush. (FWIW, the rotating brushes in the Miehle vacuum have never scratched the aluminum oxide finish on our hardwood floors.) We have wool wall to wall carpet in the bedrooms, hardwood in most of the house and tile in the kitchen, entry areas, and baths. To prevent the spread of dirt as much as possible, we keep runner carpets at the entries and basically behave like Japanese people, no shoes in the house. When we bring in groceries, we drop them at the end of the runner rug and then take off our shoes when we move them to the fridge. We keep weatherproof sandals or flip-flops outside all the exits and use them when we go outside and take them off before we come inside. The Japanese figured out a long time ago that's the best way to keep floors as clean as possible. Easy, fast, and effective cleaning? Isn't going to happen in house the size you have. My wife or I spend at least 1 1/2 hrs. every week just vacuuming and cleaning floors in a 2100 sq. ft. house. Then there's tile mopping after that.
We purchased a well reviewed steam cleaner and used it for years. As time has passed, it's become our opinion that they are best kept and used to clean up after a spill or for spot cleaning. They are VERY slow to use for cleaning an entire house if you do it right. I would strongly advise you talk to a reliable flooring store in your area, consult Angie's List, etc. and find a local carpet cleaning service that knows what they're doing. They don't charge that much and their industrial equipment is going to do a way better job than a puny home unit.