They gave me free creative freedom with my design. I ended up looking at American Football team mascots and the style of using an animal with some bold outlined text. This style led me to consider the name Raptors and to use the Velociraptor genus as the team mascot.
I started creating the text part of the logo in Illustrator first, starting with a font and using create outlines to allow me to edit the size and structure of the font. I then added a dark outline to the text to make the green stand out more and to match the outlined American Football team style. I also gave the text a shadow, by copying the layer behind and connecting the edges to the shadowed darker text layer behind it. I finally gave the text a slant and readjusted the first R to make it match the other more fuller at the end of the word.
I then moved onto the graphic of the mascot, starting with an outline of the shape of the head of a Velociraptor then adding more detail and outlines to give the face more structure and shape. I finally added some feathers by instruction of one of the team members and made it breath fire to make the mascot seem more fierce.
The final design is below. I am happy with the outcome and will definitely try this style again in the future as it was a good learning experience and gave a good result.