If you want to digitally record yourself in a room (not a real studio), and have it sound any good, you need 3 things.
1) Decent software (bbillings, this may be your problem - most people I know who record videos use Audacity or a DAW to record the audio, then mix it with the video - or use a standalone recorder/camera, of which good ones are quite expensive).
2) A good mike stand.
3) A curtain, or an open clothes closet, or a large piece of foam on a music stand, behind the mic. (Or spend money on one of those mike stand absorber things...)
Then stand 3-4 feet away (about a meter) and play. Almost any condenser mic will sound very similar to what you sound like if you do this. You have to watch your recorded levels, make sure they are hot enough but not too hot, and everything will be fine. If you stand very close to the mic, most condenser mics will be so bright sounding that they will be harsh, and maybe even distorted (saxophones are LOUD). Dynamics, like the Shure and Heil ones described do better close up, but this method still works with them.