I've had both Dish (past) and DirecTV (current) and they've both got different advantages. To get all the channels, Dish requires two dishes (one south and one SW). DirecTV only requires one, but it requires a much larger view opening to the SW as it picks up several satellites along an arc. They both offer different advanced options in 3D or 4K programming, though they never seem to keep the special channels for long. Also, both compress the local broadcast feeds, so you're better off watching local channels using an OTA antenna, especially for football games.
Yep, you'll need another source for Internet with both.