Delightful old pistol.
The pistol shown in this thread is a 1911A1. The 'access' cuts on the frame just aft of the trigger guard identify it as such. The 'A1' modification started in 1924, so it cannot be older than that. Some G. I. pistols had the 'cross hatched' triggers. From the photos, that pistol looks pretty much as issued. Collector's value in that pistol; probably secondary to family value. I wouldn't part with any gun that had belonged to either of my grandfathers. (I don't have any, but...)
Fine (0000) steel wool and most any lubricant will typically remove the rust without removing the finish underneath. Do NOT use a 'rust remover' like Naval Jelly; it will take off the rust and the finish! (I don't know if Naval Jelly is even sold anymore.)
CLP - breakfree - is a good general purpose lubricant and protective coat for metal. For actual cleaning, I prefer Hoppe's #9 as it seems to remove most powder residue and other gunk without being too harsh on either the gun or one's hands.