How to professionally delete background of an image??

[6thSense]

I am working on this book cover in Illustrator, and I am having problems deleting the background of this one image (in ps). I use the magic wand, but it doesn't look smooth me.

I have this image of some rings on a white background I got from stockx or one of those sites. These rings need to sit on an image (which is a large monogram M). I am trying to make the background transparent, and my attempts....well, they are ok for the average eye, but for something going to print, it just is not good enough. I am still learning illustrator, so I am trying to delete this background using photoshop. I used the magic wand to delete the majority, and then tried to use the eraser to clean up. Still looks like garbage to me.

I became so frustrated I thought about about a diff approach from deleting the background. I would just create the "M" in one layer, dupl the layer, crop it, etc etc. Only prob is when I try, transferring back to Illustrator makes the image jagged. And trying to crop in Illustrator? Well that is like calculus to me.

Is this making any sense? lol. Any suggestions? Any easy way to do it that I am just overlooking, or another approach that stands out to you?

[chomper]

Its all about the pen tool. Here is a tutorial i found on google, check it out.

http://www.melissaclifton.com/tutorial-pentool.html

At first the pen tool seems tedious, but once you get it, you'll be flyin...

[Gaussian]

We need to see the image before we can make a suggestion for one or more techniques.