Hi Craig
Welcome to a hobby which has given many of us a lot of enjoyment.
Cleaning up a neglected gun can be very rewarding but be sure to use proper techniques to avoid any damage to your new find.
0000 steel wool and automatic transmission fluid is a good safe bet to clean off old gunk and light surface rust.
Stay off the wood, avoid getting any oil on the wood.
Depending on how comfortable you are disassembling and reassembling mechanical objects, use your own judgment.
Sometimes complete disassembly is required but exercise caution, the project can quickly become more involved than originally bargained for.

Those 'rails' are referred to as top and bottom ribs.