AppleTV has no tuner - you watch one thing at a time. One AppleTV would be needed for each TV.
AppleTV started as a vehicle for playback of iTunes store material, photos and music. Subsequently in the black models participating 'channels' have been added from various providers however many of these require separate subscriptions to those channel provider's services.
You can rent movies from iTunes or buy them. TV Shows can only be purchased - rentals were iniotially allowed but no longer.
AppleTv is a mish mash of things these days but it currently has no PVR capability so if you need that it would not be a good option.
Current model has no storage, original did. Only purchases from iTunes store can be archived by downloading in iTunes.
As far as the streaming services go they vary by country so you need to check exactly what is on offer in your country (US I assume):
You watch the streaming services live - we have fewer in the UK but Netflix for example is rate adaptive so quality is proportional to internet speed - slower speeds get worse quality - I'd imagine you are getting 5Mbps not 15 Mbps (check at speedtest,net in a browser).
As I understand, one can watch TV shows the next day sans rental, or if using Hulu Plus. But I was thinking of a kluge (workaround) whereby one could save streams to a external hard drive available to all within range of Air Port, such as the big Airport Extreme.
I expect we'll see some exciting Apple TV innovations within the next six months. I'm an ever faithful member of the "cult" since 1988.