How to best keep dust out of my system?

Hi,

I recently built a myself a new pc and lately I noticed quite a lot of dust in my room and some in my old pc. I am somewhat worried about my new system since I heard dust can be quite problematic for components! My new system´s case is a Fractal Design Core 3000 which is poorly manufactured and not exactly dust resistant. Now I have already placed my system on top of my desk rather then on my floor which should help but are there any other good ways? Im not really ready to invest a lot of money in pre-built dust filters and fancy compressed air cans e.t.c. mainly because I have a feeling I could probably do a good job myself with old stockings or simply covering some of the holes up...

My case has very good airflow, I have two fans in the front directing air in (1x 140mm and 1x 120mm - the 120mm is blowing partially into a hdd compartment) (these are protected by dust filters already) and one 120mm fan at the back of my case blowing air out, as well as a Cooler Master Hyper 212 Evo for my 4670k and my Gigabyte GTX 770 has three fans (windforce) cooling it.

Now my problem is I have two more 140mm air vents on the top of my case and a 140mm on the side panel which are the main problem since dust can easily float in... Could I simply cover them up or would that be a bad idea?

Any help is greatly appreciated, thank you!

Btw, I do have 2 Cats which like to sneak into my room once in a while and they do like to leave their fur behind, as far as I know this can also contribute to the dust?