If you’re serious, then get a name-brand double-action air brush with a tip/needle size around .35mm. Gravity fed will allow you to use very small volumes of paint (which makes that type more economical for details and small jobs - most scale models). Siphon feed brushes generally offer larger paint reservoirs, but unless you regularly build really large models, it’ll be rare that you’ll need that much capacity. But if you do build large models, siphon feed is an option.
Somewhere in the 1/4 -1/2 oz paint cup size is totally adequate for most scale modeling. Smaller cups need to be filled more often, larger less so. If you’re mixing custom colors, you should mix the color in a larger container (recycled paint jar, etc.) so that refilling your airbrush paint cup doesn’t require mixing new batches of that custom color (to maintain consistency).
Badger and Iwata are probably the most commonly available brands in the US, but any other name-brand brush (Paasche, Grex, Rich-Pen, etc.) will be more or less equal in quality. Differences lie mostly in subtle “human factors” like how the brush fits in your hand, the “feel” of the trigger, etc. I have Badger, Iwata and Rich-Pen brushes in my “toolbox.” I use each one for different types of work, so another consideration is just that - different types of work may require different types of airbrushes. However, the vast majority of my scale model work is done using my Rich-Pen 213C with a .3mm tip. All of the other brushes are usually used for jobs that my Rich-Pen is not suited for.
You will read and hear advice that you can buy a cheap, no-name import airbrush from some discount tool store that will “work as good as any…”. Although there is always a grain of truth in such advice, in general this is a poor option for anyone who is serious about using an airbrush. The fit, finish and quality of these “tora-nocka” airbrushes is all over the place. Occasionally someone gets a really good one, but most often they’re just glitchy, fiddly, and frustrating. The argument that they’re cheap enough to just throw away (i.e. they’re essentially disposable) is a false economy for any serious painter who really cares about his or her craft and art. My personal advice is to stay away from these.
Learn proper double-action airbrush trigger control right off the bat. Better to learn the right way than to try to un-learn bad habits later. Down-Back-Forward-Up. Turn on the air, then the paint. Trun off the paint, then the air. This sequence will GREATLY help with eliminating or mitigating “tip drying” and spatter. With practice (and a reliable source of air) you should learn to keep the trigger depressed and just pull back and push forward to control the paint flow from off to full. PROPER TRIGGER CONTROL IS ESSENTIAL TO GETTING THE MOST AND BEST OUT OF YOUR AIRBRUSH.
Small compressors can be noisy, but if that’s not a problem, you can get away with cheaper ones. “Silent” small compressors tend to be more expensive. In either case, you should always drain the tank after every session to avoid leaving water condensation sitting in it (which promotes rusts and collects other contaminants).
I use a Silent-Air 20A in my studio in our house, but in my large shop, I use an 80 gal Ingersol-Rand. Whatever you use will need BOTH a pressure regulator (with gage) and a filter/moisture trap.
You can use compressed CO2. Commercial compressed gas suppliers (Air-Gas, Prax-Air, etc.) and near you can discuss the options, but there are several standard small tank (cylinder or “bottle”) sizes that are convenient. You might also consider checking with soft-drink vendors who supply restaurants and bars. They have regular route services that re-fill/re-supply compressed CO2 at the customer’s location. (I use Air-Gas for welding gas for my “big” shop.) Once you have a “bottle,” - you’ll pay a deposit the first time - re-fills are done by exchange, empty bottle for a full one. The gas “re-fills” are generally pretty inexpensive once you’ve paid the deposit.
“Thinning” (or most correctly, reducing) paint for spraying is not subject to a “one and done” formula or ratio. With experience you’ll learn the reducing ratios (paint to thinner or reducer) that you use most often, but different application goals and paints require different thinning ratios (along with adjustments for air pressure, paint flow rate, distance from the surface and speed across the surface). Hence, there is no single best thinning ratio that will work for all paints for all jobs in all ambient painting conditions).
I can (and would happily) tell you what I normally use. But unless you’re spraying Tamiya acrylics using Tamiya X-20A + Tamiya Yellow Cap Lacquer Thinner out of a .3 mm tip airbrush, what I do might not work at all for you. For close-in detail work I use a totally different mixing and thinning protocol than I do for general base coating both of which are different than what I might use for free-hand camouflages or painting with stencils.
In the end there is no substitute for experience, so get a good, name-brand quality airbrush. Match that with a reliable and controllable compressed air source and start off using a name-brand line of paints formulated for scale modeling along with that manufacturer’s proprietary thinner / reducer for that particular line of paints. Stick with your choices until you have “cracked the code” and mastered them to squeeze every bit of performance you can get out them. When you reach that stage, you’ll know enough to make informed decisions about changing airbrushes and paints to get what your earlier kit is not giving you (or that you can get all you need or want from what you already have).