If you already have a regular-sized food processor, you can grind meat using the small metal blade. You just pulse it to the right consistency, making sure not to over-process.
I have used both a hand grinder (my Mom's) and a food processor, and I much prefer the food processor. I find it easier to control the amount of fat in the ground meat using the processor. One year we used the food processor to grind up odd bits of venison for a friend who bagged a deer--if you have a hunter among your family and friends, it is worth bearing in mind.
I have really vivid memories of the time I decided to grind up liver in the hand grinder--not a pretty sight!