Also important is to know that if you are looking at a setup that includes speakers in the $400-$700 then that's a home theater in a box kit, not a 'receiver'.
Using Denon as an example...
These are receivers:
https://usa.denon.com/us/product/hometheater/receivers
No speakers, no subwoofer, nothing else. Just an A/V receiver.
Looking at one of their cheaper models, this is certainly in line with what you are asking about:
https://usa.denon.com/us/product/hometheater/receivers/avrs720w
It has half a dozen HDMI connections. They will work with Blu-ray Disc, cable TV, Roku, Chromecast, AppleTV, a laptop (or computer), etc. Basically, anything with a current HDMI connection on it should work with the receiver and it will amplify audio to your speakers, and pass video on to your TV.
If that budget includes the need for speakers, then this conversation is going to get a lot longer, because you will need a receiver AND speakers, which will just need to be properly budgeted.