You have a 52" pool.
3" of sand is just fine. 2" is ok too, if the dirt under it is perfectly smooth.
Putting the sand in first is a good idea, unless you have a machine big enough to dump it over the walls into the MIDDLE of the pool.
I would go with the peel and stick foam cove. Easy to install, consistent angle around the bottom of walls, and won't be damaged during installation of liner.
Liner:
You will pull your hair out trying to put that old liner in, although I don't know what kind of hairstyle you have, or if you have any hair at all. I tried to put the original liner back into my 24' beaded 3 times. Just barely streched it enough to get it into the bead receiver, and then it was at least 6" away from the walls, more near the cove. When the water got about 1/4 up, it started collapsing the metal walls. I thought " the liner came out, and i'm getting it back in ". Boy was i kidding myself. They just shrink too much. Save yourself the time, energy, and expense and get a new liner. I can almost guarantee you will have to anyway. And besides, you get to choose the pattern that YOU want.
Hope this helps.
Benny