IMHO, the necessities are a new GK and CB and it seems like TS is a done deal so now the CB is an absolute must this summer.
As far as the #9, another MF and a defensive fullback, I think we need to make up our minds first about what we are going to do with our youth players first before we make movements in these areas.
I think a big reason why we have been reluctant, especially with the #9 situation is that A) we already have too many forwards in the squad atm and B) not wanting to make another Ibra-sized transfer gaffe. Players like Montoya, Sergi Roberto, Dongou, Bartra, Tello and eventually Deulofeu all find themselves with rather nebulous and ambiguous places on the team.
The problem is the lack of variety. In my opinion, Tello and Sanchez are pretty much the same player while Pedro has very similar attributes to them, except he is a bit more intelligent and better in possession than both. When Deulofeu comes back, that's four players who all do very similar things competing for one spot next season and this lack of variety can hurt us when games don't go our way like they did against Valencia. Out of Tello, Sanchez, Pedro and Deulofeu, I think two should leave to make some more room in the squad for forwards we need.
This sort of problem though will continue to compound itself as more and more youth players begin to break into the team. With Rafa, Denis Suarez and Samper possibly coming in next season into the MF, we need to discern whether or not we are going to truly implement them into the team or not bc if not, we need to be proactive this summer. Time is ticking and the options we need will get picked up if we don't move.
IMO, players like Dongou, Bartra and Sergi really need to get a run of games at the top level to see if they can cut it. Those three players have the potential to be exactly what we need but we need to give them an actual look to see if we need to go into the market at all.
We need decisiveness and a long-term plan to help transition this team into our next evolution. More of the current stagnation will continually push us in the wrong direction.