In addition to that, get the app iReal Pro. Within this app, you will find some additional options to download songs. Do that.
There is also an option to purchase different playback styles. Do that, too.
The Real Book has the melodies.
iReal Pro has the playback functions, as well as learning tools including transposition, tempo alteration and the ability to loop a particular section. Also, during playback, there is a cursor that shows you what chord you are on. At first, I found that extremely helpful.
Improv does not need to be a long and difficult learning curve. Play the melody. Then add some notes around the melody. Then play a counter-melody.
If reading chord changes is something you need to work on, play arpeggios.
IRealPro will be very helpful with these steps.
Final advice - play the songs you like. No need to start with the weirdest stuff coming out of our local jazz school. And no matter what you are improvising, be sure to play an actual melody. Use your degree.