This mascot will be for print media only (ie. does not need to be animated).
A 3/4 view perspective is where the object is seen at an angle that is somewhere between front view and side view (see the image below for an example pose that is in 3/4 view perspective)
About the vector graphic question, All I need is the ability to resize the image (up or down) without distorting it or losing quality. As Pyrite mentioned, if you can export the image in a format that is compatible with Photoshop, then we should be fine.
Finally, it's important to realize that the style of the mascot should not look to 3D'ish. My aim is for a cartoon styled graphic like the ones on the example site I gave you, not a 3D model per say.
Tesla[1up]