I wasn't quite sure where to post this, as it's something that I've written without really having a thread that fits it, but this seems to be the best option.
I'd prioritise three signings in the summer. Centreback, centre midfielder, centre forward. The centreback, I'd be looking for an experienced player with good on-the-ball skill, a calming influence. We've got Bailly, who's physically very impressive, who you could argue is moving towards being a Vidic equivalent, well we need the Ferdinand then. I'd prefer not to name names because my knowledge of football outside of the Premier League is limited, but either of the main Spurs partnership of Vertonghen and Alderweireld would be nice (although not very realistic).
The centre midfielder could go one of two ways. You could look for a Michael Carrick replacement, somebody to sit in that holding midfielder position and look for the pass, or you could go for someone who plays a similar sort of role to Herrera when he's asked to play more defensively, that fast-moving, intercepting style of play. There's a very obvious candidate for the latter style, and he's just won the PFA Player of the Year Award for Chelsea, so we're probably not getting him. I think either of those styles could work, but I'd lean towards the second. I think a partnership of Herrera and a Kante impersonator in a sort of defensive midfield position would allow Pogba more freedom going forward (and Herrera could always move forward if this new player is more defensively minded and can cover). You're effectively looking for a Carrick replacement anyway, it just depends on whether you go for a like-for-like or not. I actually feel like the sort of player I'm talking about could be Fosu-Mensah, but Mourinho obviously doesn't feel the same way.
Finally, the centre forward. The Griezmann rumours won't go away, so if it's him then I think you want to play him with Rashford or Martial so he's got a partner, and you hope that if he doesn't' score, then he's setting up the other. If not him, then a lethal goalscorer now that Zlatan is almost certainly done. If whoever's in charge of buying and selling at Bayern suddenly went insane and wanted to give us Lewandowski, then that'd be lovely. An outsider option that's emerged fairly recently is Mbappe, but I think every top team is going to want him, so you can't really put all of your eggs into that basket. A somewhat unrealistic option (as if I'm being realistic by naming Lewa) would be to have Martial on the left, Rashford up front, and then someone like Ousmane Dembele on the right. He's only just joined Dortmund, so I wouldn't say that's something that's going to happen, but that's a front three that would be absolutely terrifying for a defender, with the pace and skill involved.
Apart from that, maybe a leftback, as this is a four signings thread. I think Shaw's early departure today has made that a more likely possibility.
I'd like to see Fosu-Mensah (who I've already mentioned) play more, and I'd like to see Andreas Pereira given more time when he returns from his loan. I'd also look to move on the likes of Rooney, Fellaini and probably Phil Jones.
I realise that I've almost completely ignored the point of the thread. so if I had to name names, and again I'll hold my hands up and say this is with a limited knowledge, and sort of hovering between a "someone like"/"realistic signing" mindset I'd say:
1. Van Dijk
2a. If you want a "Carrick" then I think Weigl is the most "alike" from what I've heard.
2b. If you want a "Kante" then personally I like Everton's Gueye, but I think Nainggolan of Roma could do that job very well (this is an opinion based almost entirely of going on FM17 and doing a search for players with good tackling/work rate/stamina).
3. Griezmann (just because it seems so obvious that it's happening
4. This is meant to be a leftback, but I'm drawing a bit of a blank. I'll just say Mendy because I feel like I'm obliged to say someone from Monaco.
I think that allows for a number of potential XIs/formations.