I'm a zoologist and I think it's a great profession. So the the simplistic answer is that you can go as far as you want! If you want an academic career where you drive your own research goals then you will ultimately need a PhD, but focus on getting a good degree first and then (assuming you are in the US/Canada) get on a good masters program.
As far as other options, yes I think you could be a game warden with just a first degree. You could also work for a professor as a field researcher, or work in a zoo. I would say that all jobs in zoology are hard to get and competition will be fierce. Who wouldn't rather watch lions in the Serengeti than sit in an office?
My advice would be to get some practical experience which will usually mean seeking out volunteer opportunities. Also, if you want to work with animals then be prepared to work with any animals not just exotic or charismatic ones! When we are recuiting field workers (or volunteers) we look for people with field assistance, not for people who love our study species. This means that volunteering with small scale local projects is usually your best bet for getting involved in bigger things later.
As for double majoring... I'll let someone from the US comment as to whether they think that's a good idea. My advice is always to study what you find interesting - if that's microbiology and zoology and you can handle the workload then great.