1. Receivers typically list their power as something like this: 90 watts per channel at 6 ohms, 120 watts per channel at 8 ohms.
Speakers typically list their power ratings something like this: 15 to 100 watts recommended power. As long as your receiver's output falls
within the range of the speakers recommended power, you'll be fine.
2. Cost ratio depends on your goals. I prefer mid-level receivers as they tend to have the best bang/buck for me. How much you want to
spend on speakers shouldn't be influenced by what receiver you have, if you have a mid-level receiver. It's best to determine your budget
before you start asking for speaker and receiver suggestions though.
3. Denon, Onkyo, Yamaha, Pioneer, Marantz..All of these receivers are pretty well regarded. Each have different features but all are
basically equivalent in performance. As long as you get a receiver with room calibration capabilities, you'll do well. Most would probably
just tell you to avoid Sony.
4. I doubt this would be a problem for you, but make sure that the impedances match between the receiver and speakers. For example, using
4 ohm speakers with a receiver rated for 6 or 8 ohm use, could cause problems. I doubt this would be a problem, but it's really the only
issue to look out for.
5. Many receivers have HDMI passthrough to allow your devices to play on your TV without having the receiver on.