I think the best choice vegetables for a juice fast (or feast) is to use a wide variety of juices to ensure you're getting a broad spectrum of nutrients.
Carrots, Cucumbers, Lettuces, Cabbage, Bell Peppers, & Celery all juice very well.
You can experiment with different blends, I like Carrot by itself, or with celery or lettuces. And lettuces, caggage, cucumber, are good mixed together and the bell peppers add a lot flavor to those green mixtures.
And remember to break your juice fast sensibly, just as you would a water fast... Obviously a generous serving of chicken isn't ideal.