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This probably sounds a little dumb, but can I benefit from starting an AdWords Campaign?
Not dumb at all!
Can you benefit from more traffic?
Exactly the right question to ask.
I use AdWords to raise awareness of my not-for-profit resources site, just as your local museum might advertise "events" to get people in through its doors.
One good example among many possibilities.
To all of the above I'd add that is really important to know what "more traffic" is worth to you - and manage your AdWords account accordingly.
If you decide to give it a try, I'd advise starting small until you've gotten the hang of things. Maybe try just a few keywords which are tightly targeted to a well-written about the exact same thing. Then send the user to the right page on your site, and work towards understanding if this extra traffic is working to your benefit. If it is, then think about growing the campaign...
One key point: never set your daily budget higher than you are comfortable spending. If the system suggests a higher budget, you need not go with that. If it does suggest a higher budget, though, it probably means that you have too many keywords - or that the keywords are too general.
BTW, one cool thing about AdWords is that there is no minimum term of service, nor is there a minimum spend.