Air Compressor

It is a starting point. And a good combination for the Badger 350 that you are using. In my experience a better compressor gets better results (less pulsing and moist air) but if you are getting back into the hobby this set up is okay. Maybe along the way you want to invest in better equipment but I would focus on the basics first before spending money.

It looks like that compressor has a regular pipe fitting outlet.  A cheap moisture trap should take care of the moisture.  

My current tankless/filterless compressor does pulse like mad, but I find it does not affect the painting.  A bit irritating, but I guess that is the price I pay for a cheap silent compressor.

Don mentioned a moisture trap,I would get one of those moisture trap-regulator combos for sure,unless that's what Don meant.

Compared with Borg, Don and Tojo, I know nothing, relatively speaking.

But as another newbie here who also only recently returned to the hobby, wanted to chime in and mention that I also had a decades old compressor from the old days. I went out and bought a new one. Now think I would have had just as good a starting point had I gone out and bought a regulator, or better a regulator/moisture trap combo as mentioned by all three of the more experienced modelers above.

Welcome, btw.

Some regulators have moisture traps built in, others do not.  You can buy just moisture traps that go in series with the regulator, for those regulators that do not.  They are not that expensive.