I have read that our Sun will increase in size to a red giant. But after it goes through the helium flash it will contract somewhat. Then after that grow again to be even larger before finally losing its outer layer as a planetary nebula and becoming a white dwarf. I've seen estimates that the red giant phase will consume Mercury, Venus, and probably Earth. (Even with Earth's expanded orbit due to the Sun losing mass to the solar wind.) My question is how large will that first stage be prior to the helium flash? Which planets, if any, will it engulf?
Low mass stars like the Sun do become very large prior to He ignition in the core. The exact value depends a bit on models for mass loss from the extended atmosphere (e.g. Guo et al. 2016), but estimates of 250 times its current size are possible (Schroeder & Smith 2008; Spiegel & Madhusudhan 2012).
At this radius both Mercury and Venus are engulfed. The mass loss from the Sun means Earth would orbit a bit further out than now. Nevertheless, it too would be engulfed in Schroeder and Smith's model at that point, because tidal drag dissipates energy from the orbit and it "falls" into the Sun very quickly.
Interestingly, the Sun achieves its maximum size at the tip of the RGB, rather than in the AGB phase.