Prince2: This is for people looking to manage the project from very high level. Keeping in view that your current role is not such, I would not suggest you to go for it. PRINCE2 is nice methodology but I have found it fit for top management mainly or someone who does not deal with the details of the project and is more into seeing if the project is going fine or not - all from macro level.
PMP: My favorite (please note that I am yet not certified). In my opinion PMP certified professionals are more sought after compared to other certifications. PMP takes care of complete lifecycle of a project. If you are looking into eCommerce product manager, I think this would be best suited for you. I myself is managing an IT company where we deal with several ecommerce projects and my personal experience says that PMP certified professionals have a much better idea about project lifecycle. It has helped us keeping the projects running with least number of issues and we have been able to manage a retention rate of between 85-90% in last 5 years.
CSM: If you want to get more involved in the day today activities of the work, go for this one. Your eCommerce Product Manager profile would need CSM or PMP is very much defined by what is the size of your company (I know many people will say that how in this world did the company size come into picture, but please read on). In case your company is a start-up you are supposed to perform several roles at the same time. Since you are in techno-functional role I think CSM will be really great fit. It would keep you rooted to the ground with you getting your hands dirty with detailed level involvement in modules n system. If you are in a comparitively bigger organization where roles are defined and one person does not have to do every damn thing, I think PMP better suites you.
My progression will be:
Techno-Functional -> CSM -> PMP -> Prince2
So get certified for everything but at different times. I am not saying that you are not better-off with only one of these certifications, but the natural progression which I see has been listed above. Rest is completely your call.