one more thing both game makers allow you to post games on their sites and both(byond its easier but gamemaker can still do it) can make multiplayer games and bot can easily have game vids posted on youtube
Oh man. This is the question. You want a program that is free and easy. The former is quite easy to achieve; a Google search for "free game software" will bring up thousands of results. However, most of these are not easy to use. Flashdevelop, for example, requires a very indepth knowledge of ActionScript to use effectively.
That said, you should probably try out Game Maker Lite, and Stencyl. They are both relatively easy to use programs that aren't hard to get the hang of.
The ones I have used are not user-friendly at all, Though you can find a few nice ones on C-net or do a google search for one. Most of them are not easy to use, takes allot of time to learn how to use one.
So if you have the time to learn one then I recommend you do, its hard but can be fun once you got the know how.
There's also the 'bored out of my mind with a computer i can't install new software on' option, which is to try writing games in an Excel spreadsheet. All you need is an If() function and a random number generator. They'll be fairly simple games, of course, but can be enough for proof of concept.