Hi Challenger,
I would go for something like a Canon 2000D and a Sigma 150-600mm Lens to start with. Not sure how much it will be in the USA but it would all cost about £1000 in UK. Normally things in £ equate to dollars in the USA.
The camera is a great entry level camera and the lens is what I use for all the pictures above.
As you progress you can keep the lens and upgarde to a better spec camera.
If you don't want to spend as much I would recommed a Panasonic LUMIX DMC-FZ330 which is a bridge camera. It has all the functions an SLR will have but it has a lens you can't replace. The bonus with this camera and ones like it it has an equivalent lens of 25mm-600mm so will allow you to do all the stuff you want and also do landscapes and other stuff that requires a wide angle lens.
This will only cost you in the region of $400
I had a similar camera for several years (LUMIX DMC-FZ50) before moving to an SLR, the pictures attached are all taken with a bridge camera. For the money they are excellent. You can learn how to use it before using more complicated gear.
World Fireworks Championship Blackpool 2009 Austria 022 by
Ian Cramman, on Flickr
029 by
Ian Cramman, on Flickr
P1010185 by
Ian Cramman, on Flickr
P1010147 by
Ian Cramman, on Flickr
Hope that helps.
Ian C