but I am wondering if it is the kind of bacteria we want.
I always cycle a tank fishless unless you dont have a choice. I use a starter nitrifying bacteria like Proline or Bacta-Pur, bring the concentration of ammonia up to 2ppm and add my bacteria directly to the biofilter. I aerate the biofilter for a few hours to give the bacteria a chance to start binding to the media, then start the system as a whole. If im not using a dedicated biofilter, I add it directly to the system water and keep it running.
From there I measure ammonia levels and bring them back to 2ppm daily to make sure I have plenty of nutrients for fast bacterial growth. If at all possible, I like to keep the temperature at 80deg or above to keep their metabolism fast and let them replicate faster. As the system finishes cycling, nitrites drop and nitrates rise, I bring the temperature into the acceptable range for the fish/plants. Then I wait for the ammonia levels to drop to zero before adding the fish. If you cycled everything properly, your good to go. If you have too many fish and get an ammonia spike, it's good to have some cloram-x on hand to bind up any extra ammonia. It will make it non toxic to fish yet keep the ammonia bio-available for the bacteria so it's a great thing to have for emergencies.
Thats how I cycle