Usually people start with jazz coordination by playing snare drum independence patterns along with a static cymbal rhythm— see Jim Chapin’s Advanced Techniques, for example. It’s a thing to do, and it should be done. But it’s not the only thing to do, and I don’t think it’s the directest way to becoming a functional jazz drummer. Jazz does not necessarily require a rigidly unvarying cymbal rhythm, and complicated left hand activity.
What it does require is a cymbal rhythm played with a strong quarter note pulse. If you can do that, and play some simple things with a little creativity, you’re in OK shape as a novice jazz drummer— at least as far as pure timekeeping vocabulary is concerned.
This is a summary of a lesson item I’ve done with a number of students— adding easy things to a varying basic rhythm played on the cymbal. Use the rhythms in pp. 10-11 in Syncopation, or pp. 14-15 in my book Syncopation in 3/4. Or pp. 6-7 in Joe Morello’s New Directions in Rhythm. You could spend some extra time on the rhythms that are most like the normal ones; lines 2, 4, and 15 in Reed pp. 10-11, for example.
These are quite easy, so you can just memorize the concepts, and practice them in a free form way— after playing through them, with all of the cymbal rhythms from the books, working out the coordination with the standard hihat/bass drum rhythms.
Play the rhythm on the cymbal
The top line rhythms in the book, on a cymbal, with your right hand. Swing the 8th notes, and play them with a strong quarter note pulse, and a steady rhythm.
I’ll use those same two rhythms for all of the other examples.
Add standard rhythms with the feet
In 4/4 play 2 & 4 on the hihat. In 3/4 play 1 on the bass drum and 2 on the hihat:
I won’t write these parts into the remaining examples, but you can continue playing them while you do the other things. Or not. If the rhythms conflict with the later things, or if the groove starts suffering because there’s too much going on coordination-wise, stop doing one of the things. There’s time for punishing rigor later. Do what you can do reasonably quickly, while making the cymbal rhythm sound good.
Play both hands in unison
Play the book rhythms with both hands, on cymbal and snare drum:
Playing in 3/4, you could drop out the snare drum on beat 1— don’t hit it at the same time as the bass drum. That’s an easy way to start breaking up the left hand part while playing mostly in unison.
You can also play just part of the cymbal rhythm with both hands— experiment with that:
Add snare drum in the spaces
Play the left hand on the &s of the written quarter notes. You should do this a lot.
Bass drum at the beginning of the 8th notes
Play it on the first 8th note after a quarter note— here you might want to eliminate the bass drum on 1 in 3/4, unless the rule calls for it:
Doing this together with the snare drum in the spaces sounds good:
Bass drum at the end of the 8th notes
Play the bass drum on the last of any run of 8th notes:
Or on the quarter note after any run of 8th notes:
Where the rhythm changes…
Play two notes— SS, BB, SB, BS— where the cymbal rhythm changes from quarters to eighths, or eighths to quarters.
On the last 8th note, and the quarter note after it:
On the first 8th note, and the & before it:
There are a lot of possibilities that could take a long time if you insist on doing exhausting all possibilities in all combinations. I don’t think that’s necessary. You’re going to practice a lot of jazz independence in other formats. Do what is easy for you to work out quickly.