The only team that I will support is Everton. I hope they surprise the league and everyone like what Leicester did. Just don't know when is the right time though. 
Leicester's championship was one in a million. We won't see any other surprises for the next 25-30 years and maybe more. Manchester City and Arsenal are 2 favorite teams to win Premier League in 2017.
With Ibra moving in, the league just got tougher, but I still don't lose hope for my team even though I think they could only make it up to 5th place. Nobody knows.
Last season Arsenal he missed a tremendous opportunity to win PL. most of the favorites was very bad (Leicester are to best use).
In new season it will be much harder. Klopp is adapted in Liverpool, Mourinho come on United, City have new good manager, Chelsea also. if you add a serious team like Totenham, Southamton and possible surprise like Leicester, personally do not expect much from Arsenal.