Got any rental places around you? It may be worth it just to rent for a day or so-chainsaws are pretty high maintenance and odds are you will hardly ever use it. You will need extra chains, sharpening system, safety gear.
Weight is very important-go for as light as possible that will still do the job. A 20" bar is overkill (and overweight) for what you need-get a 16 or 18. Stihl and Husky are the best brands generally-nearly everyone else is an also ran.
I suggest you go to HD/Lowes, pick up a few different models and see how they feel to you-also check out the prices on chains, bar oil, tools, etc.
The last saw I got was a Husky sold by a rental place. Good saw, very good deal-after I essentially rebuilt it, replacing all the rubber bushings, etc. Worked great for over a decade after I got it. The only reason a saw should throw a chain is something is out of adjustment-the operator should be checking chain tension fairly often-they stretch with heat and use.
Electric chainsaw good cheap alternative but I doubt it will handle a 12 inch tree-at least not without a lot of struggle-which is a bad thing with a dangerous tool.