Luc,
You are asking the age old question on what to do next. Great question, loaded question. Currently, their is nothing on the market in terms of programming that is a direct replacement to all of what programming cable can accomplish. Cable has a platform, a channel, not so with the internet. It is out there but unorganized in comparison. If your family wants to learn as you go an increased understanding of how to get the most out of your computer by becoming more computer centered and less remote control centric, then you are on the right path.
My suggestion is to get with one brand and stay with it. If Sony is what you are into, then stick with Sony. If Apple is where you want to go, then stick with Apple for rich or for poor. Staying with a brand helps reduce the mis-understanding of what the new gadget is suppose to do while interfacing with what you already have. Eventually, everyone builds an intuitive knowledge base to at least have a clue on how things should work. When you mix brands on the surface you are mixing parts below surface in the not so long run it becomes confusing and unreliable because all of these devices have updates and performance specs whose core is either upgraded or not. If so, it may not be upgraded at the same time as everything else because it was built from a entirely different company. The way this plays out is so often a slow computer, pop windows and system operation freeze. Even for a computer its hard to work as one when know one is on the same page. The page you are on is p i s s e d because you don't have time to figure this stuff out, you need it to work and work now!! I hope you see my point, when a change is made from one brand to another different you run the risk of throwing something out of kilter. This process becomes the equivalent of electronically trying to undoing a tangled cord.
I like Apple. Apple is simple and Apple works. The service is best bar none. And they back whatever equipment you have old or new the way you think you should be treated. Google TV has bugs that still must be worked out. I would sit on that one for now until matters get sorted out. The best blu ray players on the market are gaming consoles, Xbox, PS3 these units rack up hours upon hours of use and abuse and they perform without a hitch, just ask the kids. Do you have a computer? Are you looking for a dvd blu player already to hook up to the internet. Another words, what do you already have to work with? Surely this would be the starting point. To get further down the road I can assure you the purchase of high speed internet is primo to everything working well. You don't have to get the fastest, get the middle high speed internet application then you will be good. Understand how the routers work, or be sure to purchase the same brand router. For now, their are two kinds, some routers stream audio only, others stream audio and video. Apple TV streams both audio and video. With an HDMI cord plugged into the Apple TV into the back of your TV you are halfway done. The rest of the set up will be based on establishing a password and identifying a security code.
Apple TV is buy here pay here. Cable's business model is to have you and I buy at the same rate for 300 channels even though we only have time to watch 5 channels in a month.
Having said all of that, it is entirely possible to get rid of your cable bill I have done it and many millions of others have done the same. To make the transition, your family will need to have current computer software, decent computer hardware, 1 or 2 routers, a healthy set of speakers and a plan for how you are going to watch sports. lol. So much more to the story. Hopefully this helps you some.
Best.