Go all out for Greizmann, firstly. He's the biggest no-brainer of a signing that there's been in ages. He's a United fan, and young enough to be able to do without CL football for one season. He's also the best footballer around not at a club that pays huge salaries. Also, he's not a winger as some have posted here. He's far far more suited to being a #10/second striker. Basically he replaces Mata/Lingard/Rooney/Fellaini in that central attacking role.
For ST and RW, I'd go for Ibra, and Dembele/Sane.
As for the other positions, I believe they aren't as big a priority but if we do sign players then,
CB - Giminez is the best young CB presently of the ones I've seen (no idea why he'd move though). Otherwise someone cheaper, older and less expensive. I've heard Manolas at Roma is good.
CM - Saul (in addition to Sanchez it appears, Carrick and Fellaini to go probably)
Can anyone think of a potentially top class attacking right back who is not at a big club? Darmian looks like he could become a Heinze-type solid fullback, but we could do with a bigger threat in attack.