Hi Jennie,
This is an excellent question and I think one that gets at the heart of what it is to find a job in the 21st century. I don't exaggerate at all when I say that networking is the most important part of finding any job, be it your first or your twenty-first. There are estimates based on large surveys and polling that show more than 70% of all jobs are obtained through some form of networking, not through traditional "cold applying" to jobs you find posted. In fact, there have been reports by experts (although I have not found data to back them up) stating that 70-80% of all open jobs in America are never even posted because they are filled from within or from contacts already known to the hiring company. I myself got my job through networking after applying unsuccessfully for more than 100 positions I found posted online. So, the one thing I wish someone would have told me... network well, network often, and network with anyone who's willing to talk to you. It's also important to note that many conferences where companies, NGOs, and government agencies are present will let students or those seeking employment attend for very discounted rates or even for free if you are willing to volunteer. Attending those events is a great way to meet the people who can fast track your job search. I could go on with this all day, but let's talk about some other keys to finding a job.
Make yourself stand out by broadening your knowledge base. It is true that keying in on one type of chemistry or one niche can often lead to jobs in bench chemistry, but getting jobs outside what you might consider the typical track for a chemist can often be more about the breadth of knowledge you have. What I mean here, if we are talking about green chemistry jobs, is learning toxicology, green chemistry, business, economics, global culture, and the list goes on. Obviously we cannot all be experts in all these fields, but it is worth gaining enough knowledge to be able to speak the language.
One other point I like to share is that you shouldn't limit your search too much based on the type of company or organization. When I was looking for a job and applying unsuccessfully over and over again, I was taking the strictly treehugger approach. I was applying only at NGOs, certification bodies, government agencies, and companies who's business models were almost completely focused on sustainability. What I quickly learned is that you are narrowing your search extremely by doing that, and you are also missing some REALLY great opportunities. I never really took the long view to consider that working for a large global corporation would provide the opportunity to have a much greater impact by making much smaller overall improvements. But I digress.
Anyway, I hope this advice helps, and if it doesn't feel free to ask another question. 
And oh yeah, I'm going to try to address your second question in a separate reply... so stay tuned.
