In all my encounters with Vedanta, everyone from Swami Vivekananda to the Resident Minister at my local Vedanta Society says I shouldn't accept anything they teach without investigating it for myself. At no point has my skeptical behavior been discouraged or criticized; in fact, the Resident Minister encourages me to ask her questions all the time.
But every group looks good to its own people and its own literature. I think when researching a group (of any kind, not just religious), it's also worthwhile to see who its enemies are and what they have to say. My parents encouraged me to read authors I disagree with from time to time (you may have seen the recent Friendly Atheist post on the subject). I might refine my perspective on an issue, or at least learn how the opposition thinks.
Regarding religious groups, the Advanced Bonewits' Cult Danger Evaluation Frame by neopagan Isaac Bonewits is a good starting point. Basically, if a group seems awfully concerned with perpetuating itself and taking over your life, you might want to think twice, or as many times as needed for you to run the hell away.
For information on specific groups, visit the Ross Institute's Controversial Groups Archives. Rick Ross is an expert on cults and is probably most well known for his "deprogramming" work, which is basically helping people break out of cults. He has used some methods in the past that I wouldn't advocate, but his website is an excellent clearinghouse of information on controversial groups. Note: a group's listing on this site doesn't necessarily make it a cult per se, and I don't think Ross is trying to say it is. But if certain scary patterns of behavior seem to emerge from a group, well, you've been warned.
Next time: an update on where I am in my search.