julienma Hi Julien! You and Bastien have built a really nice looking product. Love the design and product messaging. It's awesome that you all are looking at Stellar now too.
RE: polling and displaying data transaction data. I agree with tyvdh, you could link to a transaction explorer such as stellar.expert (excellent site as well), but to keep things simple it might be better to get what you need from a horizon endpoint for storage and display. You can poll for it, or your can use server side events (SSE) to "listen" for transactions. It all boils down to tradeoffs in latency and complexity. If you get really big you can run a validator, and from what I understand you can just hit the underlying tables directly with SQL - but that's probably overkill for now.
If you all need help with testing or any other technical or product assistance please feel free to reach out. I launched a Lumens only shop last week (http://stellar.shop) as a way to experiment with the platform and learn more about the needs and opportunities in the ecosystem. More than happy to share with you my experiences and help in any way I can.