Some really average players being suggested now, we have the money and status to aim much higher.
I like Begovic as a 'keeper and a man, but his biggest weakness is De Gea's biggest strength, and something that every modern day goalkeeper needs: Distribution. He's a decent, fairly cheap option, but not much of an upgrade on Valdes imo.
I'd like Lloris but he'd be expensive. Keep Valdes or take a punt on Leno.
Defensively, we need to replace Evans and Rafael. Smalling has come on a lot over the course of a season, but we cannot trust him to stay injury free. I wouldn't mind going for Hummels, or Otamendi to an extent, but don't see them as a massive upgrade to be honest as neither have been tested in this league. There is a genuine lack of quality central defenders these days, so we should go younger and build for the future. We can look at Marquinos or Laporte, but Varane is unrealistic. I'd go all out for Stones, he has massive potential. Alves is a decent short term option at right back, with Darmian or Coleman as a longer term investment.
We need to be aiming for an upgrade on our midfield, that is, an upgrade on Fellaini. Carrick and Herrera are top quality, we just need a player who can cover for one or both, or play alongside them. See Schweinsteiger, Vidal, Pogba for the high end player, or Aranguiz, Kranevitter, Kovacic for a more left field option.
We probably need another top, top winger if we let Nani leave. It seems that Bale, Ronaldo and Sterling would be a stretch, so I'd go all out for Marco Reus, love the guy. Like Depay, he can play anywhere across the front. If not, Griezmann would be a player I'd like, but again, unrealistic. And I've always like Draxler as a left field option, although he's gone off the boil a bit.
Let Falcao, Van Persie and Hernandez go, and we'll need at least one forward. If Wilson goes on loan, we'd need two. I'd try and prise one of Lewandowski or Muller from Bayern, or take a chance on Lacazette or Higuain.