I went out and bought a cheap dynamic microphone the other day from the local music store. I'm not looking for anything big right now, just a step up from my camera's on-board microphone.
I've shot a few test films, and noticed that there is a hum/buzz from the mic when recording. Whether I hear it in the headphones or not, it will always show up in the footage. I have it hooked into my camera so that it starts with the mic, then through an XLR-to-3.5 mm cable, into a 1/8" adapter, and finally into the camera's external mic jack.
When I use this mic to speak through a normal amplifier, it works just fine - no buzz/hum.
First, if you can't hear it in the headphones when they are plugged into the camera, you need better headphones. Buy Sony MDR7506 headphones at your earliest convenience.
Second, you don't provide any information as to the wiring of the 1'8" TRS plug or the input of your camera. Most cameras have stereo input jacks. Unless your XLR to 1/8" cable is wired properly, it will cause a buzz.
Third, dynamic mics are of low sensitivity. The require more gain than most condenser mics. That gain also brings up noise. That could also be the source of your buzz.
As you continue on your path and start doing projects professionally, you will learn that you can't afford to buy cheap.
They are $99 USD. Don't look, just buy. These are industry standard. They are because they are sturdy and tell you what you need to know about the audio coming in to your camera.
The XLR to 1/8" cable you have is probably not wired for stereo. You need one in which the #2 pin from the XLR connects to both the tip and ring of the 1/8" plug. Some cameras put a low voltage on the jack to power certain mics. This voltage may be useful, or may cause noise or distortion.