Based on your list or “tools” Blender is your only option to make a movie show reel. Your show reel show vary based on what you are trying to achieve. My show reel is for the end customer. They don’t care what tools I used to make it, or if the mesh is perfect, or how I used the lights, or where I made the texture. All they care is that their project is done on time and it looks good. All my show reel is, is a bunch of clips from my finished projects from 2012 put to music. The only transition I use is a cut. I could have made it in movie-maker if I needed to.
However, my show reel is pretty much useless if I am looking for a job on a production team, because there is no breakdowns, no showing different skills I might have on a production team. For this you would might want to transition between (say) a turntable of the model and a wire frame of the model to show off your modeling skills. Maybe showing your animation with the bones showing, or a breakdown of how you used the compositor to add occlusion or a specular layer or lights. So you are probably not looking so much for “transitions” but more fading one layer onto another.
Google “Blender VSE tutorial” and you will be rewarded with a ton of instructional videos that will help you learn to put together clips using fades, time remapping, and more.
And last music. For my show reel, it is important because the end user needs that. For a production team show reel you can add music, but the person watching will probably have the sound off.
Well I hope you found an answer in all that…