What is true definition of "F2P" team?

So I am planning to build a F2P Aglaea team despite that I have Sunday and Huohuo on my account. I already have an idea of the team; Tingyun, RMC, and Gallagher.

I was planning to pull for E2 and/or get her signature LC but I talked with someone on Discord that pulling for E1 and signature LC are not the true way of playing F2P.

I want to challenge myself and see what is like building a pure F2P, but it makes me wonder just how I do it.

EDIT: OK. I appreciate everyone replying to this, but I think I may have created some misunderstanding. I want to create an Aglaea team without using Sunday, Huohuo, or any other limited characters. I hope this is more straightforward and easier to understand.