I'm thinking of either the one called "DNA Ancestry Project" or the National Geographic one. Both seem reputable, and cost only around $100.

The "home testing kit" is only a cheek-swab preparation, nothing great.

By the "other half" I mean one person will only provide either paternal or maternal ancestry, and I want a relative to provide the other half, so I can trace both my mother's mitochondria and my father's Y chromosome. Which won't tell me anything about ancestors with my family name, as we are an illegitemate branch of the family.