Hi,
I am not sure how other freelancers are quoting you on budget and time. The thing is, if you want to update your 1.6 version website to latest version, that is, 2.x then we need to develop the website from scratch, as the structure of magento 1.x and 2.x are different. If you want to upgrade it to version 1.x to 1.x latest version, that is 1.9, then it will take less time.
Please let me know. I am interested in working on this project and will provide you more suggestions.
Regards,
Sangram