Creating a product, how to and where to start

So I work in a company as a software development team lead (in a way, we work with prepackaged solutions implementation with some custom development on our end, think of MS SharePoint), and my company asked us to build a custom product of our own now, and ofc this opened a lot of doors for me and I have a lot to look into, I'll list some questions I have below and please feel free to share anything i should pay attention to or keep in mind.

1- Where do I start, like I'm trying to collect the requirements and build some sort of design document and my database and code architecture, but what steps should we do differently when working working with products versus normal projects

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2- It comes to my mind that I should have some sort of release management structure/system, for versioning other aspects, I already have TFS for source control but I'm unsure how can it serve in release management area

Assuming I went with Semantic Versioning, how do I implement such strategy in my development activities, can I incorporate Microsoft TFS for such purpose? like do I create branches for different clients/versions, or whats the best practice in such cases

3- We will most likely use Agile (scrum) as our development methodology, if you have any input on that

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And if you have any other points I didn't consider and you feel that I should, please let me know, thanks in advance