Be installed by yourself if you are familiar with gas piping, have all the tools, etc. The log kits usually come with a good set of detailed instructions and an installation video. But check with your building inspector first! It may not be legal to do it in your community without a professional installation.
BUT! That aside, I personnaly would not consider a ventless unit. Even if it works properly and doesn't kill you and your family with CO poisoning, it will put a tremendous amount of water vapor into your home. Water will run down your windows from excess humidity, and you will not be happy with it. I would go with a unit that you can vent.