Your telescope will be stored for many more hours than it will be in use, and you want to keep your optics clean and free of dust. Closing the tube will also prevent mice, cats, spiders and other things from nesting in your tube (all of which we have seen photos of!). However, if your tube has just come in from a dewy observing session, it should be allowed to dry out before it is closed up - put your dust caps on the next morning, assuming it has dried up by then.
Most focusers come with dust caps when purchased. Ours did (see photo). If you need a dust cap for your focuser, you can purchase them from telescope component vendors (See our Vendor Links). If you happen to have the now rare 35mm plastic film container, these are just right to fit in a 1¼ inch eyepiece hole and were used for many years before digital photography took over.
For the tube openings, an inexpensive, if inelegant, shower cap works well as a dust cap (see photo). You might also find elastic food covers will work also. Often, telescope makers use thin plywood to make dust caps, held on my a friction fit with the tube, strong, small magnets embedded in tube rings, or Velcro.
Whatever your taste, it makes sense to have some sort of dust caps for your scope to keep it clean in storage.