Modern Singers are not the same as older Singers.
If you want to use a home grade sewing machine, I would look for older all-metal singers from the 1950s-1960s. Models of note would be 401, 403, 411, 500, 503. Used Kenmore all-metal gear machines from the same era are also a good bet. These can be had for $5 at a yard sale, to a couple hundred rehabed on eBay. Good info here:
A compound feed (walking foot, feed dogs, and needle pull fabric together) is probably overkill for making felt backpacks. These machines are best when multiple layers of thick material must be kept aligned and fed evenly through the machine. These are large, heavy and have big tables, so unless you plan on doing serious work with it, this machine is overkill for your needs, esspecially because it will not work well on light-weight fabric without significant adjustments.
I would suggest a Sailrite LSZ-1 http://www.sailrite.com/Ultrafeed-LS...Sewing-Machine
sewing machine. It is basically a home machine on steroids and is simple, tough, and durable. It is also easy to store when not in use, something not true with industrial machines. There are videos on that website of the Sailrite sewing through 10 layers of Sunbrella, a heavy acrylic outdoor fabric.
The price may seem a little high, especially compared the the computerized plastic wonders at Walmart, but this is an investment in a lifetime tool that will work on everything from light fabric to moderately heavy projects without problems.