There's no real "minimum" size for a vocal booth, in the sense that 8 feet long sounds terrible bu 8'1" sounds wonderful... it's more like a gradual spectrum, starting with "disgusting" for a close-sized booth, up to "amazing" for Abbey Road studio 1! (OK, I exaggerate just a little).
For a home studio, it's more a question of: "How much space can you spare?". In other words, larger is always going to be better, so make it as big as you can.
Small-ish booths can still sound reasonable, if treated well. There's also a saying around here: "If that's all you've got, then it's still better than no place at all!" As long as you realize the limitations of any given room that you might want to build, then you won't be disappointed after you build it, and it will serve the purpose.
I'd suggest that you start your own thread, with photos and diagrams of the potential location(s) for your booth, so we can help you based on better information.
- Stuart -