Hi,
My name is Mark and I am a Magento Developer and Project Manager at PROtech Soft.
I have extensive experience working with Magento and have built more than 100 websites. You can check my profile on oDesk which has over 1800 hours work in Magento.
I have gone through the requirements and they seem to be a little confusing. Are you looking for a Magento website with Shopify backend? If that is what you are looking for, it is practically impossible. Each system has its own interface and even if you like shopify backend, you will have to get used to Magento backend if you want a website built in Magento.
Your budget for a custom magento website is quite low though. If you want a site built from ground up, minimum you are looking to spend is $3000. In $250, maximum that can be done is installing an existing theme and setup your content.
If you need help with that, please let me know.
Thanks,
Mark