Joel,
I have dealt in antiques for over 40 years and have handled many sterling and silver plated pieces. On old large pieces sterling is usually stamped sterling and has hallmarks that indicate sterling silver content, the maker, the year made and where it was made. Sometimes the piece will be to small for the sterling mark, but will have the hallmark stamps. Many older pieces will be stamped coin silver or simply coin which indicates a silver content, but less than the .925% content of sterling. On older pieces the sterling mark and the hallmarks are usually small and marked on the bottom rim, but, depending on the size of the piece, the stamping may be in the middle of the bottom of the piece. I don't pretend to know all the hundreds and hundreds of hallmarks, but a rampant lion hallmark stamp indicates sterling. You can look up the rest of the hallmarks when you get back home.
Plated pieces are commonly marked EPSN which stands for Electro Plated Nickel Silver. The base metal is nickel with a thin silver plating.
When you wrote that you cut the piece in two and it was silver looking metal all the way through, I suspect you have a piece of EPSN.
Keep looking at the garage sales and you will find some true sterling pieces. I buy a lot of clearly marked sterling at garage sales and thrift stores. I also buy a lot of 14K to 18K jewelry at the same places for next to nothing. Some people don't realize that the pieces they are selling are gold or sterling and then others just don't care. I just recently bought a set of six silver teaspoons, that were marked "coin", for three dollars for all six. I found these in a new antique shop and I suspect the dealer doesn't know anything about coin silver. A couple of weeks ago at a local church flea market my wife picked up an 18K gold bracelet with approximately 2 karats of diamonds at a local church flea market for the grand sum of $10. It's out there if you know what you are looking for.
Randy Hedden