Wall mount speaker’s input jack

If you're installing in room where you can't drop above or below the room to run your cables, consider putting up crown molding -- it typically leaves a small channel behind it which is ideal for hiding speaker cables.

You can then punch holes in the top of the wall where you need to run vertically, fish the wires through, staple it up into the corner, then install the crown molding to hide everything.

You can also go the low route, and hide them behind your baseboards, but there isn't always a void behind them, so this could get a little messier if you have to trim away drywall (or plaster in older homes) to create a channel you can use. You also have problems with baseboards if you have to go past any doorways.

There are a million options out there. The main thing that you need in this setup is finding a receiver that has really good output control - in that you can pick exactly which outputs you want the sound to go to and be able to save those settings... So if you want to go to all rooms you would have an all-room criteria saved, and so on. You need the receiver and the monitor/module that controls it - usually sold together. Everything else is all about tastes and how much money you have to spend, and how many controllers you want - you could station wireless controllers around your house.

Don't want to get too off-topic for DIY... You need to be looking at multi-room or multi-zone receivers. Here is an example. I am not telling you this is the exact fit for you. You have a lot of researching and figuring out your requirements. There are receivers that have monitors that you could station in every room and every room could hear its own thing... lots of $$$. I would say you need at least 2 zones - living room and bedrooms... Also can you control the sound level in the bedrooms do they just have the speakers wired to the living room? If you want different sound levels each room will be its own zone.

Also 5.1 isn't a must. There are tons of surround options from 3 to 9+ speakers. 5.1 was the standard a while back and is fine. Any multi-room/zone receiver will give you surround abilities (most high end ones do 7.1 or 7.2) in your main living space.