Without the benefit on hindsight:
2013: José Mourinho - proven winner, experienced in the league, gravitas and winning mentality to fill the void left by Fergie. Followed by Carlo Ancelotti and Pep Guardiola - in that specific order. Basically, big name managers with good leadership credentials, and title winning experience - not just domestically, but in the Champions League. Preferred José and Carlo because they were/ are used to handling a big club in England, and they're more pragmatic - like Fergie, compared with Pep - who's more of a purist and burns himself out because of his intensive methods. In terms of what was wanted, Moyes didn't match any of those qualities.
2014: Van Gaal was the best choice, all things considered - keep in mind that Klopp wasn't going to leave Borussia Dortmund before the expiration of his contract, and he parted ways with the club only after the meltdown. Hasn't worked out so well thus far, but the consensus opinion was that he would build a good team and provide some sort of structure to the squad which would pay dividends in the future - and with good reason. Unfortunately, he's underperformed all across the board, and will likely leave the squad in a disjointed state.
2015/ 2016: Ideally, we should've started negotiations with Carlo once he was sacked by Real Madrid. He fits the bill almost perfectly, we wanted him after Moyes was let go, and he is a superior manager to Van Gaal - said as much in the Van Gaal extension
thread. Unfortunately, United were enamored with Van Gaal's foundations when there weren't enough tangible signs of progress; and Bayern were super decisive, and Pep is joining City. José Mourinho is the only remaining candidate out of the traditional Big 3, and as luck would have it - he's currently unemployed. Fully expect the club to make an arse out of a perfect storm though. That's been our modus operandi in recent seasons. Might sound harsh, but it is what it is. José is the easy choice coinciding with the right choice - so to speak, especially in terms of what we need at this moment in time, IMO of course. But nah, let's overlook one of the 3 greatest managers in the last 20 seasons because he doesn't meet every single criteria in our exhaustive list - even the rudimentary ones.