Welcome to the forums John.
Yes, the LG you’ve picked is going to be compatible with your computer. It is an IDE/PATA interface drive like your old ones.
You can replace the two drives you have now, or just replace one of them if you like. I like to keep more than one optical drive on hand, if for no other reason than to reduce wear and tear on the dvd writer.
But many people just use one optical drive in their systems.
The only tricky part about replacing IDE interface drives is to get the little jumper on the back of the drive set correctly. If you are only going to have the one drive, put the jumper on Master setting, and connect to the IDE cable on the very end connector. You should also examine the IDE cable and make sure you are using an 80 wire cable, not the old style 40 wire cable.