One interpretation among many possibilities. I marked the right hand legato and the left hand quarter notes staccato. These would be 'wet' staccato, or "portato". Slightly detached, but marked to give the music some forward momentum.
James Maddox present another lovely rendition closely resembling the edit above. He places less emphasis on the broken chords in measures 9 and 16 though.
You've got to learn your instrument. Then, you practice, practice, practice. And then, when you finally get up there on the bandstand, forget all that and just wail.
I'm a professional pianist and music educator in West Toronto Ontario. I'm also a devoted percussionist and drum teacher.