Hello there,
My name is Bojan I am freelancer from Macedonia/Europe.
First I would like to let you know that Magento 1.9 and 2.0 are two totally different things.
The Magento 2 Is not an latest version from 1, it works way too different.
The option that I am recommending you, is a part from your option A to upgrade your Magento 1.4 to the latest Magento version 1.9.2.4
There are a lot of extensions that you might need later on, and there are a lot of extensions available that could help you out to increase the sales.
Modifying the current version and debugging it, is not a good solution and I am not recommending it.
With Magento v1.9.2.4 you will be able to install the latest Quickpay extension and any other extension that you want, because most of them are compatible with this Magento version.
I will work on my server, the new vs old site will be easy comparable.
The budget that you have purposed is way too low, I don't know if it was just a placeholder.
If you want to save your time and get a quality feel free to contact me.
Best Regards,
Bojan