Audio and video pass on the same HDMI cable, so they generally are synced pretty good.
When you bypass the audio out, receivers usually have a feature called "lip sync correct" where you can adjust the lag audio wise.
My Motorola cable box remote is capable of turning "everything on". Just hold the power button for 5 secs and it powers all the devices on/off.
Also keep in mind, like Smart TVs of the last couple years, receivers have really blossomed too.