What we'd like to happen
Someone comes in and makes all the right noises - strong willed, active in the transfer market, not afraid to put a few noses out of joint to get the job done. Although Zajec remains at the club, he moves into the "upstairs" role he was brought in for and we rarely hear about him, only occasionally in regards to the setting up of an academy or some scouting exercise. Meanwhile, the new manager has a completely free rein to bring in his own players, pick his own teams and decide his own tactics. He wins and loses off his own back and is the clear figurehead of the club. This doesn't mean the end for Joe Jordan by default, he's clearly a decent coach and it seems a lot of fans would like him to stay. Obviously, a clear favourite for this sort of approach would be Gordon Strachan or Claudio Ranieri - another possibility mentioned after his sacking from Valencia.
What could happen
Whilst the new manager has something of a free role, there's still a system of "reporting back" in place. Jol and Arnesen do it at Spurs and it's a common enough theme in Europe; the "head coach" takes charge of the team and picks the players, but still has to listen to advice from a Sporting Director (or to use the Anglicised version, Director of Football) on certain matters, in particular transfer targets and who comes into the club. Obviously this could rub some people up the wrong way, but the likes of Koeman and successful Dutch manager Co Adriaanse, who have both managed in Europe, would be used to this system and would probably not be too bothered. The normal problem in those sort of working arrangment comes about when the manager is there BEFORE the DoF and never wanted to work with the man above him in the first place; Rix and Redknapp, Redknapp and Zajec for example. But if they know the situation they're stepping into, it shouldn't be so much of an issue.
What will probably happen
Nothing will be in place by the end of April, and it'll be the start of the summer before the move is finally made for a coach. Chances are it will be someone we haven't heard of before and a good friend of Milan's and Zajec's. I have to point out that by being unknown doesn't automatically make them bad - a lot of people scoffed at Adriaanse before realising he had a very good record as a manager - but the "friend" bit is the problem. It'll be a puppet manager, a yes-man, whilst the decisions are made above his head and just has to be the public face. A bit like Joe Jordan now in that respect; has a say, does a bit of coaching, but at the end of the day it's out of his hands and realistically Zajec is in charge. For all we know it could actually work - we've hardly had much time to judge Zajec and it's been a time of immense strife for the club - but it's not what most fans would like to see.
As much as I hate to disappoint people, I can't see an almighty big name coming in and lifting spirits. After all, who is there to choose from? If people are expecting some big euphoric release as everything is magically changed in the summer, it isn't going to happen. Evolution rather than revolution, I'd dare say. But that's not to say it's all bad news - even the last possibility described above, which to many would be the "worst", may well end up working out for the best in the end. In a year's time we'll be able to look back with hindsight and pick at what we obviously would've done better, but I don't envy those who have the choices to make.
Still for now we can only assume and second-guess the real intentions at Fratton.