I'd like someone with a bit of independence, their own ideas not built by being part a Pep Guardiola-infused cult - perhaps even with some experience of playing football at a decent level.
Most of all a bit of humility.
Honestly nowadays, I think this is becoming less and less relevant. Modern management is a complex task - requires a thorough understanding of tactics, statistical analysis, training methodologies, sports science etc. etc. For the most part, it's the footballers that realize they're not going to make it big and start honing their managerial skills at a younger age that seem to make the best managers. Most top players are getting to it too late, and trying to rely on their name and reputation, rather than any particular management ability.
Mourinho, Wenger, Klopp, Frank, De Zerbi, Potter, Emery, Postecoglou, Howe, McKenna, Appleton etc. etc. (and, yes, the snake himself) - all either had journeyman careers that ended early, or barely played football at all.
Pep seems to be more of a rarity in this era in that he was a genuinely top class player before becoming a top manager.