Here are my remarks of your following points
1. Complete catagory section (1 catagory is complete for reference point to replicate to other catagories)
==>Ok,can be done... let me know what category structure is pending
2. Swap out few home page banners
==>Ok
3. Set up payment gateway (Paypal/ Global Payment)
=>Ok, need credentials for gateways
4. Sync all product images from old website to new website. The products have already been transfered
==>Ok, I will use magmi tool for faster import of images
5. Insert brand banner which will also be responsive with the website
==>Ok, can be inserted and also will make it responsive
6. Insert 3 new links/ pages from re-directed from banners on homepage
==>Ok
7. Transfer favicon from old site.
==>Ok
8. Create couple contact forms for pages.
===>Ok. I will use email form module which is can be used to make customizable contact form.
Let me know... if you are ok with my quote...
Thanks in advance and happy to help you