My name is Li Ming
I think Raspberry PI 3 is good choice to build your project.
As you know , there is Ethernet and wifi in raspberry pi.
btw, i have one question in your description.
The Video recorder will be connected to Internet ?
if internet is not available , need to use extra device such as sim card to wifi adapter.
and, you mentioned about software in your description.
I suggest mobile app as software to send instructions to Raspberry PI
So, Mobile app can send instructions to Raspberry PI via internet(if use sim card to wifi adapter , internet is always available).
Also, i suggest H264 Video encoding because you mentioned web camera in your description.
Web Camera can be connected to Raspberry PI.
I already had experiences in real time video streaming between Raspberry PI and mobile app using Web camera.
And , Online payment function is not problem in my side because i already integrated online payment function in some shopping app development.
Please contact to me and let's discuss your project more in detail.
Thank you for reading my proposal.