I think the key word here is cheap - A cheap plucker will not last long. I would say the answer to your question really depends on how far you want to take your meat bird endeavor.
It's a question of economy when it comes down to it. What do you value your butchering time at? How much time do you spend butchering in a season? If you had to pay someone to butcher your birds - how much would you pay them?
We butcher almost 300 birds a year on our farm right now including 40 turkeys. When you factor the time in that it takes to pluck one chicken (about 5 or 10 minutes for one person) - we would spend an equivalent of 25-50 man hours plucking each season. We pay our crew $15/hour so thats $150 dollars extra that we would have to pay out each butchering day - $750 per season. Looking at it from a slightly different angle, that's about $2.50 added to the cost of each bird. And that's assuming that a turkey takes 10 minutes to hand pluck, just to make the math easier. So for us, it was an easy decision. We spent a couple hundred bucks on a good plucker and it paid itself back within the first season.
That being said, if you're only raising a small batch of birds, one time per year, then maybe hand plucking is the way to go. It can definitely be a good family activity - the more hands plucking the chicken, the faster it will go. But i haven't ever seen a cheap alternative to a good plucker do anything, but cause frustration and dashed hopes.
Burning or "singeing" the feathers off will not work, that is a method for getting the small hairs off the skin after the bird is plucked.
