Dear friend, I am Joomla Developer and expert about upgrading Joomla system. Please check my review to see a number of upgrade task I have done. I am glad to make perfect project for you
About your project I have some specific questions
+ How much data do you have on system : amount of articles, users, other records..
+ Do you use any addtional component such as K2, CB or JoomSocial, RSForm, Virtuemart....?
+ Can you send me your current website links? I want to see
+ We will secure for entire system? Because will have much work must do : Prevent Spam bot in Submit comment, captcha, permission in resource...
What is my plan
+ Install new fresh system . So of course no malware, virus on it. No backlink...
+ Install all components, module and plugins you want
+ Move data from old system to new system ( records, media, image, user, articles....)
+ Install a fresh template and make the same style like old template. I don't use old template or any code from it so we can ensure code is fresh
+ Secure the site
+ Make Akeeba backup for full site
I am sure about what I will develop and ready to share you updates for each step daily to ensure you follow the progressing of project.
I work full time so we can discuss anytime you want
Best regards
Linh