I think Spurs should probably not buy many players and instead increase the wages of their best ones. It is inevitable that Manchester United will try to buy Kane and inevitable somebody is going to make a big bid for Alli, so they will need to massively increase the wages of those two players at some point in the next few years.
Liverpool on the other hand have to start getting rid of players who aren't good enough far sooner than they do. They have an enormous wage bill and a lot of it is because they don't let their academy players leave when they won't make it. Their budget will probably increase massively regardless of that and Anfield is going to increase capacity to 60k. Klopp performed a heroes job getting a few of these players to be playing for a top four side. If it was up to me I'd sign Salah and van Dijk/Koulibaly first thing. It's also nice that they have some academy players who are ready for the team and don't need to be loaned out.
For City it's not about who they buy for me, they will need to be more aggressive and prepare for more physicality. There were many performances this season where they were too content to probe around the defense. When Liverpool played them at Anfield was a good example of that, as was their home match against Chelsea. Teams that over attack are always going to be vulnerable on the break, so unless they signed Boateng and Bonucci it's not like they're going to be fantastic at the back.
Chelsea's the best team, but they are getting a little old and need some reinforcements. Nothing further to add about them.
United is much the same as City, but make no mistake they are going to spend an absolute load of money. I think their approach is too tentative these days. Football has fortunately become a lot more attacking over the last five years and they have quality, but they need central defenders. Although, as I just said, unless they buy Boateng and Bonucci they are still going to have problems with balancing defense and attack.
I don't even know what to say about Arsenal at this point. But I do believe that it isn't possible to win the league with Wenger anymore. So I don't know where they go from that. I don't think they have enough great players anymore and I don't think they can get them in one summer. I also don't see someone as good as Sanchez staying around because he's too good for that, and there's no way they can replace him. That all being said, they finished with enough points to finish top four in almost any other season. That's still not good enough anymore though.
All of the six teams are pretty good so it'll probably come down to who has the most convenient fixture list. It's strange but one season after Leicester I think we're further away than ever before from that happening again. The top six sides this year were miles above the rest.