I am starting to develop a logo, but I want to know the best medium to work with. The size of the logo should never have to exceed 500 x 500 pixels, so I'm not sure if that should be taken into account. I would like to initally model something after this image here:
They use some depth and lighting effects to really make it pop. Should I work with multiple programs to complete this.
Just as a note, I am talking about the text that says "LinuXMint"
Firstly, a logo should always be in vector format. What you are trying to make is a 3D visual of that logo.
Judging from the picture, I'd say this is done in Cinema 4D. But could be any 3D programm really. The effects are basically extruding a path (the logo) and applying a fillet. The material shaders are probably tweaks of some default plastic and metal shaders. No reflection map was used. As for light, there is one shadow-casting spot and ambient occlusion (plus global illumination perhaps). All of this can be done in one programm.
Now I am not sure if that tells you anything as I don't know your skill level. But if you are trying to find a tuturial, at least you have the right terms to look for.
The best designed logos are NOT 3D. Many have 3D versions for things like advertisements, but they all have an official 2D logo.
Here is a list of opensource software that might be useful:
I have used Blender before, and it is a really good piece of software, and the first one I would recommend to anyone.