one note about your filter.
you need to change the "media" or stuff inside the filter from time to time (every month or so)... Your fish store will help you with getting the correct replacement media.
The white stuff is filter floss. When you replace the media in your filter, save about half of this filter floss, to mix with the new floss. This will instantly seed your freshly cleaned filter with the bacteria you mentioned. Doing this regularly will keep your filter operating in peak condition.
It is a fine filter for a tank your size, combined with regular water changes.
If you're concerned about the quality of your water, leave it sit for a few days where it can get some sun. This will help break down some toxins that might be present, but this is not completely effective.
Best of Luck to you and Welcome to Aquarium Advice!