How big will the Sun be once it becomes a red giant? How much of the solar system will it engulf?
This is answered in How fast will the sun become a red giant?. I'm just adding a note here because it's not answered directly in a form a non-expert might spot.
The maximum size of the sun is estimated to be 256 times it's current radius, the Earth's orbit is 215 times the sun's radius - so it will consume Mercury, Venus, Earth and a bit of the way toward mars.
It's a little complicated because as the Sun expands it losses mass - large stars blow off their outer atmosphere. With the Sun having less mass it's gravity is weaker and Earth's orbit moves further out. The linked paper says (if I read it correctly) that the Sun will expand first, passing the Earth, before it has lost enough mass for the Earth to move far enough away.