Great question. in either path, I would still run a pilot group that has your most technical people across various departments to test and see level of effort your org will need to complete a roll out.
We absolutely encourage you to run a pilot - but recommend including people from a variety of roles across your organization to ensure you validate the experience and requirements for your users are met. Then moving as a big bang or in sequenced phases will depend based on the needs of your organization. I encourage you to join our Upgrade Planning Workshops at https://aka.ms/SkypeToTeamsPlanning, specifically the "Identify your upgrade approach" session in which we go into considerations, including all at once or phased, for upgrade approaches.
We are just starting a 3 month Teams pilot with HR, Communications, a developer IT team, as well as our IT infrastructure department. We scoped our pilot to a Skype replacement only so online meetings and chat, with milestones for recording meetings and uploading and file sharing, then lastly Planner. We are running it for 3 months and just starting it on Monday. We already have a bunch of questions around how to handle data classification and government retention polices that we have to meet. So we as a SharePoint support team are learning along side the pilot. We aren't in 365 yet as an org we are moving from SharePoint 2013 and trying to rebuild our intranet at the same time to SharePoint online. I also gathered together some of the best links to videos from MS to get started with training and notes about naming conventions and things like that for our company. So its like a training/governance page that I just built in a communications site and then pulled into teams as a tab. I plan to run the first group through it on Monday. We also started a 365 Early Adopters Team in teams and made it a public team so anyone can join. We plan to host channel online meeting where we demo what teams can do and as a space to take questions from staff about teams and how to use it as they run through the pilot. Hope this helps.