Should we pre-purchase our tickets for this site?
Is it worth hiring a private guide to get a better understanding of the cistern and/or Blue Mosque?
Because it is a mosque, there is no entry fee for the Blue Mosque. The only rule is that you can't visit during prayer times. I probably wouldn't bother with advance tickets to the Basilica Cistern, but I haven't visited in recent years. Others who have visited more recently might be able to give you a better perspective.
We hired a private guide for Sultanahmet, including the Hagia Sophia, Topkapi Palace, and what little one could see of the Blue Mosque during renovation. (The Basilica Cistern was still closed for renovation.) I had been to Istanbul several times previously and didn't much need the guide, but my traveling companion appreciated it. If it's your first visit to Istanbul, a guide can provide a lot of background and context.
Thanks for your practical advice. I don't think we need guides for the Blue Mosque or Cistern as I see how well written up it is nin the RS Guidebook.