Those are all good questions.
I'll see if I can help. There are lots of better painters and airbrushers out there than I am, hopefully they can chime in too.
First off for actual airbrushes, I would strongly recommend a gravity fed brush, meaning the cup is on top of the brush and gravity pulls the paint into the brush to be sprayed. They work way better than the siphon fed brush you have in the webpage you posted. They are much harder to keep working right in my opinion. Beyond that, most airbrushes will do a good job of basecoating and doing some secondary colors. I personally have a badger airbrush, the renegade krome. It works really well for me and it's probably a better airbrush than I need. But badger makes lots a good and affordable utility airbrushes, similar to what you need.
Next is the air compressor, which makes a big difference in how your painting goes. The one that you have listed there looks like an identical copy to my own, and I love it. The only issue is that the motor can get pretty hot during long painting sessions. I have a floor fan that I run to help cool it. You want it to have a tank to store air, rather than one that has a continuously running motor. I had one of those and it was a hassle.
As far as paints go, there are lots of different options. I use the minitaire brand from badger and it's amazing for me. There is also Vallejo model air that a lot of pros use. I never have. I also use some generic airbrush paint from hobby lobby, they have big bottles of black and white for good prices, then you can mix any shade of grey from that and store it in extra bottles. As for using GW, or P3 for that matter, paints in an airbrush, you will have to thin the paints down. I have used a 1:1 windex to water mix that was ok. I have read about an alcohol to distiller water mix on a pro painters site. There is dedicated airbrush paint thinner to be found all over the web. You could also use a straight water to think the paint, but that could mess with how well the paint lays down. Windex and alcohol are good because the evaporate quickly and don't stay wet on the model and don't dilute the pigment to cause spidering of the paint when it gets sprayed.
As an aside, I also use a drying retarder when I airbrush because Az air is so dry. When the paint sprays out of the nozzle it dries on the needle tip and starts to gum it up. It can block paint flow completely or create weird spray patterns. Eventually it means more time cleaning your brush than painting. So that's something to think about too.
I started with a kit like this and it worked great for basecoating 40k tanks and once try models. It saved so much time on my red Blood Angels. The first time i used it I was sold. http://m.ebay.com/itm/390593716868?nav=SEARCH
Hope that helps. If you have any more questions feel free to ask here or pm me.