Hey, Guiwee, glad to see you've made the jump to an airbrush, though I'd have advised you to go right ahead and invest in a quality airbrush and compressor. Oh, well, you can always do that once you find out how much fun airbrushing is and how awesome the results can be.
If a paint says "airbrush ready" then it is exactly that. Thinning is something you'll have to decide for yourself. Some modelers say thin to the consistency of 2% milk; however, I don't drink milk and haven't for many years so I only have hazy and distant memories of what its consistency is. I usually tilt the paint jar to see how quickly the thinned paint runs down the side; if it takes time to descend, it is too thick. (Does that description make any sense?)
If you are using Tamiya acrylics, then use Tamiya's thinner. I use inexpensive lacquer thinner for all other paints. I don't usually thin Tamiya's spray can paints after decanting them unless they've been sitting for a while. I've heard it said that some of those TS paints benefit from a little bit of lacquer thinner, but I don't know which colors in particular those modelers are talking about.
Anyway, start out with some practice parts so you can get the feel of the airbrush before you try it out on a real model. I consider my airbrush the most important thing I've ever bought for modeling and it is just about the most fun part of building in my opinion. I love painting with it.
By the way, I have a single-action Badger 350 I'd let you have for cheap if you are interested. I bought a Paasche double-action, internal-mix VL and never use the Badger anymore.