Not being an expert, I'll chip in separately. In your situation I'd be using a couple of bucks' worth of electric whipper snipper. Starting and maintenance are then rather easy. Your small area (and small perimeter) mean that you don't have much of an issue with the electric cord. Incidentally I am not suggesting a battery-powered device - that just recreates the maintenance problems we are trying to avoid. A simple, brand-name electric snipper should trim up your fine grass around the perimeter in a couple of minutes, for hardly any money and even less trouble.
Why do I have a miniature petrol-powered trimmer myself? My trimming is partly along the back fence, and some pretty powerful vegetation based in my neighbour's yard comes under the fence. 3 mm nylon trimming line cannot make an impression - I'm about to try a blade on it. I did try an electric trimmer on it for a while, but after burning it out twice I decided to get real. I don't see you having this kind of problem.
