I appreciate that you have included the colour scheme and basic design layout, your preparation makes this a simple project and speeds up the design process.
For this project I would begin by tracing the original Vector image in Illustrator, creating a large scale document in Photoshop and importing the vector components in order to retain the clear definition of the original. I would find a font that resembles the original type used (you may of course provide your own font or a link to the original) and apply the font to the logo. I would then create the background ensuring the use of the colours defined in the colour palette and ensure all components are set neatly and centred to form the final logo design, saving the original psd document (all layers named and organised) as well as all the required deliverables in png format.
I am confident that I can provide what you need for this project, quickly and to a high standard. I hope to hear from you again in the future, please feel free to contact me through Freelancer.
Best of luck finding the right person for the job.
Chris.