The engines come from the factory with a muffler. You can play around with other mufflers to get it quieter. To keep costs in check, you'll probably want to source a used engine. Maybe try your local Craigslist before going to Ebay. Don't overlook complete implements. These engines came on compressers, power washers, pumps, tampers, mixers- all kinds of stuff. Be wary of generators though. They use a tapered PTO shaft that is not conducive to mounting a clutch.
The alternate option is to buy a "clone". Get a coupon, and you can have a Predator from Harbour Freight for under $100. They are basically a Honda GX200, so the Propane parts will work. Other clones are available from varying places, all for a lot cheaper than even a used Honda. Obviously, the Honda is superior- but the clone will get the job done for 1/2- 1/4 of the cost.