I own a D3s, D600 and D800E. As mklass wrote, the D3s or D4 are ideal for indoor sports, but they may be over your budget. I bought my D3s used for just under $4,000. Between the D600 and D800, I would strongly recommend the D600. It has a somewhat faster shutter rate and the files aren't as (unnecessarily) large. There's really nothing about the D800 that's better for indoor sports. Maybe a slight (!) improvement in noise, but not that much.
In any case: rent! I'd go to someone like borrowlenses,com and rent both bodies for the same 3-day weekend. It will be money well spent. Don't rent a D3s unless you're prepared to fall in love with it. That's what I did and it ended up costing me just under $4,000.