If you use standard paints like Citadel, Vallejo Game/Model Color, P3, Reaper etc. then yes, you will need to thin them before you can put them through the airbrush. There are different things you can use, all of which have different results. Personally, I use Liquitex Airbrush Medium for the job, but you can also use thinning solutions available from Vallejo, or even just water. The alternative is to buy paints intended to be used as they are without thinning, such as Vallejo Model Air and Badger Minitaire, although you will find your choice of colours much more limited.
In terms of equipment, I use the compressor from an £80 airbrushing kit on eBay, which works rather well. The one you've got there only goes from 0-18psi, which is a bit on the low side. I would suggest looking for something that can do 0-30, and if you can get one with a tank then it would be a slightly better option as you don't have to have the compressor running constantly and you get a more consistent airflow.
This is pretty much what I started out with, then shortly after I got a Harder & Steenbeck Evolution Silverline brush with 0.2mm and 0.4mm needle/nozzle kits, which pretty much covers everything I have wanted to do so far. I would definitely consider the above compressor, as it would be more suited to the kind of work you would be doing with models (some paints and primers really need a higher pressure to get working properly).
I think that may be the first significant contribution I've made to this thread in the best part of a year.