Do you or any other team member have experience in building a decision matrix for product selection? If yes, those who know how to do it should teach the others and lead in finding a way to split this activity into tasks so that the load is shared.
If you don't have experience in that area, you will need to come up with some ideas or get an expert into it - doesn't have to be an external specialist, but could be someone in your organization who has experience in procurement decision processes.
I don't have experience in that area but I would think that an iterative process could do it:
- Retrieve available product descriptions / feature lists of products under consideration (this can be split up)
- Match features and aspects of products so you can compare (team activity)
- Check with stakeholders which features are most important for comparison (team lead in meeting with stakeholders?)
- Rinse and repeat to fill in features that are not known yet for some products but may be important.
The order could probably be changed, for example if you already have a list of important features that might help to come up with the right search terms and questions for step 1.
Regarding your specific questions about who should do what: this is something the team should decide. In a previous version of the question you mentioned Scrum, but Scrum does not have a team lead or client lead role. If you're the Scrum master it's possible that you shouldn't do development tasks but depending on the team structure it might still be helpful to do them anyway. Without knowing your team, nobody can give you definitive advice.
