Neil,
The eos650 will do fine for video. If you have a wide angle lens like the 18-55 kit lens, that should be all you need for camera and lens. You haven't specifically said what type of music video you want to do. Is it just setting up a camera on a tripod to record a performance of one or more people, and put it on youtube? That is fairly simple but you will still need to edit the audio and video, add titles and credits.
Generally for music it would be best to have a stand alone recorder and mic to record high quality audio. I use a Zoom R16 8 track as a stand alone recorder which has a very nice clean sound, though you might be able to use your computer as a recorder. In a music video, the audio is probably more important than the vdeo.You can get a decent condenser mic and mic stand used for about $75. You can EQ the audio, add echo, etc in an audio editor, and mix it down to a stereo track. Then you can sync it with the camera audio and mute the camera audio in the editor. You may not need multiple takes. In the video editor I use, I use a 2 to 3 second film dissolve transition before and after the closeups. Using Adobe Premiere Pro CS6, you can alter the lighting, simulate a spotlight, change the scene lighting, tint and color saturation, and zoom in and around the video frame (like cropping a still pic) on the vdeo to do close ups in the editor. As long as you record the video in 1080P (1920x1080 resolution) there's lots of ability to change what is in the frame by zooming in and around the frame. The Adobe Premiere Pro video editor links with Adobe Audition, their audio editor, so you can edit audio and video on the video timeline. Lights may not be necessary either. You can use room light and raise the iso to shoot in room light. I always shoot video with a tripod. I have a nice tripod I got for about $40 a couple of years ago that works fine. Your budget is plenty to work with. If you can do your video in 30 days, you can get a full version 30 day free trial of Premiere Pro and Audition on the Adobe website. Your i5 computer with 16GB of RAM will work fine, though rendering a 4 minute video after you have done all your edits may take an hour or two. I've done a number of videos of me and a friend playing and singing music to put on youtube, just for fun. I just did a 2 min 30 sec video this week. It took about an hour to set up the equipment and do a video and audio check, 5 minutes to record it, a couple of hours to edit it, and about an hour to render it.
Here's a link of one I did a few years ago. All the different camera angles were done in the editor from a single wide angle video taken in room light in a single take with a Nikon D3100. You can also see the film dissolve transitions. The instrument amps were mic'ed and the amp mics plugged into the recorder, and there is one audio mic. If I am recording just myself, I'll plug the instrument directly into the recorder and use a mic for the vocal, and use headphones to hear the instrument and vocal going into the recorder.
View: https://www.youtube.com/watch?v=ZGtxpVLxCf4
