I've got a Badger 200 as well that I've had for about 12 years or so. When I decided I wanted a DA brush I got an Omni 3000 (siphon feed) and a few months ago added an Omni 4000 (gravity feed). I think I made a wise choice and have never looked back.
I prefer the 4000. Since it's gravity feed it will feed reliably at slightly lower pressures than the 3000. The 3000, on the other hand, will use all your existing 200 bottles and caps. Additionally, your hoses will fit the Omni series so you won't have to get a new hose. The Omni is actually made by Thayer and Chandler, but Badger owns that company now.
Your existing compressor will probably work just fine, however I'd highly recommend adding a regulator and moisture trap to it. Most airbrush compressors put out around 35 psi or more. For airbrushing on models I seldom use more than 15 psi and frequently go down to around 5 or so.