You want to filter the air coming into the compressor.

I agree with mike kaiser....and yes,in my opinion, a filter is worth the effort. I don't know the type you have....I used one of those foam "cut to fit" filters. When it looks dirty, I take it off and bang it against my leg a couple of times and put it back on. In my environment, I've only had to do this about 2 times a year. You should pull the tank drain plug often to get the water out.

That makes sense, I don't know if there is any sort of filter on there now, but the filter I have now is made to be installed in the line going to the tool, ie on the compressor output. One obvious use would be for blower wands if you are repairing sensitive equipment, so you are not blowing contaminants everywhere....