Bird in the hand - multiple offers

I'm a chemical engineer with some decent business experience and have been somewhat frustrated with opportunities at my current company (mostly the lack of development, even as a "high-potential").  I started interviewing for other positions a month or two ago, and recently interviewed for a position that I was really excited about.  The job turned out to be not everything that I'd hoped, but I still think I could be happy there and it would be an improvement over my current situation and provide good future opportunities.

The company made me an offer last week and wants an answer this week.  I have another interview next week as well as a couple of promising leads for jobs that I think would potentially be better for me.  I tried to get the company to let me get back to them a week and a half later, after my other interview (I mentioned this) and GMAT test, and they said they just couldn't wait that long--they have several qualified candidates and need to fill the position quickly.

So what it comes down to -- do I go with the bird in the hand, or turn down the offer hoping for something better?

Another factor is that the offer in hand would give me my first role as a manager, although it would be light on engineering, and another position may not give me that opportunity (or may give me the best of both).  I've been dying to implement the things I've learned on MT, but just haven't had the chance.

I welcome your comments.