The two main providers of DSS satellite service in the US are Dish Network and DirecTV. My suggestion is that you start by visiting the websites of both, compare the various packages, decide which one suits you, and go for it. Some links to get you started:
DirecTV packages
How to get DirecTV
Dish Network Packages
How to get Dish Network
Happy hunting, and be sure to check out both sites for their latest special offers - they both run all kinds of promotional deals that you will probably find very handy...
According to their FAQ, there is satellite based Internet access available, but they recommend their DSL service instead. This implies to me that their satellite Internet access is probably not very good.
DSL's a reasonable alternative to cable (it's what I use, because I can run a web server on it), but I wouldn't use a satellite connection unless it was your only option. Last time I looked, you have to connect via dialup and receive data via satellite, which is pretty much a kludge and I don't think it's popular with consumers.
In short, I'd keep your cable modem. As long as you want cable TV, it's your fastest and most economical alternative.
Hope that helps.
D