I don't mean to be rude, but let me say this.
If you have not tackled your first one, it may be a bit much to state that you will be learning a number of them.
Also, I imagine the sheet music would be quite expensive (if you bought it) because it is going to be scored for an orchestra. Long passages of the score will not even include the piano, because that's true of most concertos -- there ARE such passages. Take the first five minutes of the Emperor Concerto, for one example. Long passages of orchestra, more or less preparing for the piano to come in. Do you want to pay for all this? And I am not sure how valuable any version would be that omits the orchestra, if you could even find such a score.
Third, there will be some passages that can be played as a solo, but most of the concerto will be written to combine piano and orchestra. How this will sound with the piano alone is uncertain.
Fourth, concertos are showcases for pianistic talent, and most are gosh-darned difficult.
Could you possibly mean "sonatas" rather than "concertos"?