This will be fun! (For you, and for us.)
That's a healthy budget--you should be able to cover things with room to spare.
For stones, a 1K (or 1200) and a 5K or 6K would cover most normal sharpening. Maybe a 400 or 500 for major work or repairs at some point. And I'd suggest a strop (Marko Tsourkan on here makes nice wood mounted felt ones).
Have you considered a slicer or paring knife? Those are two standard knives in a kit.
You can get a very nice gyuto for 400-500. If you buy a used one (some offered here are barely used), you can try something out, and likely sell it for close to what you paid if it turns out to not be quite right for you. Or you could buy new, and have a similar option to move it on, if needed.
Jon Broida's (from JKI) youtube sharpening vids are very helpful.
Filling out the "new knife" questionnaire will help you focus on your wants/needs, and give folks here more info to help guide you in the right direction. Here it is: http://www.kitchenknifeforums.com/sh...estionnaire-v2