Connecting 3 devices at once

1) Typically the amplifier or "AV Receiver" will have multiple inputs and you select with using the remote control. The reciever will route the signals but DO YOUR HOMEWORK and be certain the reciever does i fact have all the inputs you will ever need.

Ok, Some TV sets have lots of inputs and you can connect everything to the TV anf then run the TVs audio output to an amplifier and then to the speakers. This works but it means you need to have the TV one to hear anything

Before you buy anything find the product's web site and download the user manual. Read it going as far as to draw a diagram of how you will connect it up. Normally you have many options but I'd subject to make it easy look for equipment that will allow you to use HDMI for "everything" then go to monoprice.com and buy a half dozen hdmi cables

2) $500 is a "way low" budget for a 5.1 speakers system. If you are budgeting I would invest 1/2 of the total budget in speakers. When you add up the cost of all those electronics boxes what do you get? That is a reasonable speaker budget.